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seminario Beneventano domani
by Beatrice Meini 12 Jan '26

12 Jan '26

Buonasera, scusate lo scarso preavviso. Domani alle 14, in Saletta Riunioni al Dip Matematica, Pierfrancesco Beneventano, un nostro ex studente e ora post-doc a MIT, terra' il seminario: Edge of Stochastic Stability: SGD does not train neural networks as you expect it https://www.dm.unipi.it/en/seminar/?id=694aba9c2ac7f6b23978e5a0 Saluti, Beatrice

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Fw: Talk by Davide Palitta - January 19th
by Fabio Durastante 05 Jan '26

05 Jan '26

Dear all, I am forwarding the announcement below from the FLorence OPtimization talkS (FLOPS) mailing list, as the topic may be of interest to many of you. Please find the details of the seminar hereunder. Best, Fabio ________________________________ Da: FLOPtalks <floptalks-group(a)unifi.it> Inviato: lunedì, gennaio 5, 2026 4:02:44 PM A: FLOPtalks <floptalks-group(a)unifi.it> Cc: davide.palitta(a)unibo.it <davide.palitta(a)unibo.it> Oggetto: Talk by Davide Palitta - January 19th Dear colleagues and friends, we are pleased to announce the next seminar of the FLorence OPtimization talkS (FLOPS) series. Davide Palitta<https://www.unibo.it/sitoweb/davide.palitta>, RTDb at Università di Bologna, will give a talk entitled "The S^T-S-SVD and Applications". The talk will be on January 19th at 11:00 a.m. in Room 119 Centro didattico Morgagni<https://g.co/kgs/uuxpeDA>. The abstract of the talk is available at the following link<https://sites.google.com/unifi.it/floptalks/home?authuser=3> (as well as in the attached poster). Best regards, Margherita & Marianna -- You received this message because you are subscribed to the Google Groups "FLOPtalks" group. To unsubscribe from this group and stop receiving emails from it, send an email to floptalks-group+unsubscribe(a)unifi.it<mailto:floptalks-group+unsubscribe@unifi.it>. To view this discussion, visit https://groups.google.com/a/unifi.it/d/msgid/floptalks-group/9e7571c1-e9ab-…<https://groups.google.com/a/unifi.it/d/msgid/floptalks-group/9e7571c1-e9ab-…>.

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Fwd: Talk by Simone Rebegoldi - December 11th (FLOPS)
by Fabio Durastante 04 Dec '25

04 Dec '25

Dear all, I am forwarding the announcement below from the FLorence OPtimization talkS (FLOPS) mailing list, as the topic may be of interest to many of you. Please find the details of the seminar hereunder. Best, Fabio -------- Messaggio Inoltrato -------- Oggetto: Talk by Simone Rebegoldi - December 11th Data: Thu, 4 Dec 2025 07:33:55 -0800 (PST) Mittente: FLOPtalks <floptalks-group(a)unifi.it> A: FLOPtalks <floptalks-group(a)unifi.it> CC: srebegoldi(a)unimore.it Dear colleagues and friends, we are pleased to announce the next seminar of the FLorence OPtimization talkS (FLOPS) series. Simone Rebegoldi <https://unimore.unifind.cineca.it/resource/person/113208>, RTDb at Università degli studi di Modena e Reggio Emilia,will give a talk entitled "On the convergence and stability of multiscale decompositions for imaging inverse problems". The talk will be on *December** 11th at 11:15 a.m. *in**Room 007 Centro didattico Morgagni <https://g.co/kgs/uuxpeDA>. The abstract of the talk is available at the following link <https://sites.google.com/unifi.it/floptalks/home?authuser=3> (as well as in the attached poster). Best regards, Margherita & Marianna -- You received this message because you are subscribed to the Google Groups "FLOPtalks" group. To unsubscribe from this group and stop receiving emails from it, send an email to floptalks-group+unsubscribe(a)unifi.it. To view this discussion, visit https://groups.google.com/a/unifi.it/d/msgid/floptalks-group/d52c826d-332d-… <https://groups.google.com/a/unifi.it/d/msgid/floptalks-group/d52c826d-332d-…>.

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HPSC Colloquia - Darya Majidi - L’Intelligenza Artificiale per costruire un futuro digitale, etico, ed inclusivo
by Fabio Durastante 13 Nov '25

13 Nov '25

Inizia il ciclo di incontri “HPSC Colloquia”, organizzato dal dottorato in "High Performance Scientific Computing”, in collaborazione con il ciclo di incontri "Matematici al Lavoro", in cui I nostri studenti hanno l'opportunità di confrontarsi con professionisti e scoprire le diverse carriere verso cui i percorsi formativi del nostro ateneo possono portare. Scrivo per ricordarvi del prossimo appuntamento, che sarà Mercoledì 19 Novembre alle ore 11:00 nell'Aula Magna del Dipartimento di Matematica, e online al link: https://meetings.dm.unipi.it/b/luc-bw9-xim-ayo Ospite dell'incontro sarà Darya Majidi, President UN Women Italy - Fortune Italia Most Powerful Women 2023 - CEO Daxo Group - Founder Donne 4.0 - Italian/Iranian Entrepreneur with 30 years in digital transformation & AI - Board Member - Speaker - Author. Darya terrà una conferenza dal titolo: "L’Intelligenza Artificiale per costruire un futuro digitale, etico, ed inclusivo" (di cui l'abstract è riportato sotto) L'incontro si concluderà con un dibattito e una sessione di domande e risposte, un momento prezioso per interagire direttamente con l'ospite. Tutti gli interessati sono caldamente invitati a partecipare. Non esitate a rispondere a questa email per ulteriori informazioni. Cordiali Saluti per HPSC: Luca Heltai, Giuseppe Felici per Matematici al lavoro: Stefano Galatolo, Silvia Gazzola, Marco Romito Titolo: "L’Intelligenza Artificiale per costruire un futuro digitale, etico, ed inclusivo” ABSTRACT L’intelligenza artificiale rappresenta una delle più potenti trasformazioni della nostra epoca, capace di ridefinire non solo i modelli economici e scientifici, ma anche i valori fondamentali che orientano le società umane. L’intervento propone una riflessione sulla costruzione di un’intelligenza artificiale al servizio dell’uomo, etica, trasparente e inclusiva. Verranno affrontati i temi di machine learning, reti neurali, etica, bias nei dati e e dell’importanza di un approccio multidisciplinare che integri competenze tecniche, etiche e sociali. L’obiettivo è stimolare nei ricercatori una consapevolezza critica e un impegno attivo nella progettazione di tecnologie che promuovano equità, sostenibilità e rispetto dei diritti umani.

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[Indico] Kai Bergermann, Numerical linear algebra meets multiplex networks, 13/11/2025, 11:00 Europe/Rome
by fabio.durastante＠unipi.it 12 Nov '25

12 Nov '25

Title: Numerical linear algebra meets multiplex networks, Speaker(s): Kai Bergermann, Scuola Normale Superiore, Date and time: 13 Nov 2025, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Department of Mathematics (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/329 Abstract -------- Multiplex networks are used to model complex systems from myriad applications. They generalize classical complex networks by recording different types of relationships, different interactions, or changing interactions over time between the same entities in different layers. They possess natural linear algebraic representations in terms of structured matrices, which makes efficient numerical linear algebra techniques a valuable tool for their analysis. In this talk, I will present contributions to multiplex network analysis relying on matrix function approximation and nonlinear spectral methods. I will discuss centrality measures, the solution of stiff systems of non-linear differential equations with exponential Runge--Kutta integrators, un- and semi-supervised community detection, and core-periphery detection. All presented methods have a linear runtime scaling, which allows the treatment of large-scale multiplex networks and numerical experiments for all considered problems will be presented. -- Indico :: Email Notifier https://events.dm.unipi.it/e/329

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[Indico] Prof. Luca Heltai, An overview of non-matching coupling algorithm for High Performance Finite Element Applications, 11/11/2025, 14:00 Europe/Rome
by fabio.durastante＠unipi.it 10 Nov '25

10 Nov '25

Title: An overview of non-matching coupling algorithm for High Performance Finite Element Applications, Speaker(s): Prof. Luca Heltai, Università di Pisa, Date and time: 11 Nov 2025, 14:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). Address: Largo Bruno Pontecorvo, 5, 56127 Pisa PI You can access the full event here: https://events.dm.unipi.it/e/333 Abstract -------- This seminar presents an overview of non-matching coupling algorithms for high-performance finite element applications, with emphasis on implementation and preconditioning aspects. We address ficitious domain, immersed boundary, and mixed-dimensional problems on non-matching grids, as arise in coupled PDE systems defined on heterogeneous domains. We derive different formulations and show how most of them can be traced back to variations or stabilizations of the Lagrange multiplier and distributed Lagrange multiplier frameworks. We discuss various implementation aspects of the problem, including exact and inexact integration across non-matching grids, matrix based and matrix-free transfer operators, particle-based transfer operators, and discuss briefly some augmented Lagrangian-based preconditioners, designed to yield optimal and scalable convergence properties when used in conjunction with iterative Krylov solvers. Finally, we discuss what is the current status of the implementation for these solvers within the deal.II finite element library. StreamingThe seminar will also be broadcast online at the link: https://meetings.dm.unipi.it/b/luc-kwc-keb-p9k Note ---- Reminder -- Indico :: Email Notifier https://events.dm.unipi.it/e/333

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[Indico] Prof. Luca Heltai, An overview of non-matching coupling algorithm for High Performance Finite Element Applications, 11/11/25, 2:00 PM Europe/Rome
by fabio.durastante＠unipi.it 06 Nov '25

06 Nov '25

Title: An overview of non-matching coupling algorithm for High Performance Finite Element Applications, Speaker(s): Prof. Luca Heltai, Università di Pisa, Date and time: Nov 11, 2025, 2:00 PM (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). Address: Largo Bruno Pontecorvo, 5, 56127 Pisa PI You can access the full event here: https://events.dm.unipi.it/e/333 Abstract -------- This seminar presents an overview of non-matching coupling algorithms for high-performance finite element applications, with emphasis on implementation and preconditioning aspects. We address ficitious domain, immersed boundary, and mixed-dimensional problems on non-matching grids, as arise in coupled PDE systems defined on heterogeneous domains. We derive different formulations and show how most of them can be traced back to variations or stabilizations of the Lagrange multiplier and distributed Lagrange multiplier frameworks. We discuss various implementation aspects of the problem, including exact and inexact integration across non-matching grids, matrix based and matrix-free transfer operators, particle-based transfer operators, and discuss briefly some augmented Lagrangian-based preconditioners, designed to yield optimal and scalable convergence properties when used in conjunction with iterative Krylov solvers. Finally, we discuss what is the current status of the implementation for these solvers within the deal.II finite element library. StreamingThe seminar will also be broadcast online at the link: https://meetings.dm.unipi.it/b/luc-kwc-keb-p9k -- Indico :: Email Notifier https://events.dm.unipi.it/e/333

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[Indico] Kai Bergermann, Numerical linear algebra meets multiplex networks, 13/11/2025, 11:00 Europe/Rome
by fabio.durastante＠unipi.it 03 Nov '25

03 Nov '25

Title: Numerical linear algebra meets multiplex networks, Speaker(s): Kai Bergermann, Scuola Normale Superiore, Date and time: 13 Nov 2025, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Department of Mathematics (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/329 Abstract -------- Multiplex networks are used to model complex systems from myriad applications. They generalize classical complex networks by recording different types of relationships, different interactions, or changing interactions over time between the same entities in different layers. They possess natural linear algebraic representations in terms of structured matrices, which makes efficient numerical linear algebra techniques a valuable tool for their analysis. In this talk, I will present contributions to multiplex network analysis relying on matrix function approximation and nonlinear spectral methods. I will discuss centrality measures, the solution of stiff systems of non-linear differential equations with exponential Runge--Kutta integrators, un- and semi-supervised community detection, and core-periphery detection. All presented methods have a linear runtime scaling, which allows the treatment of large-scale multiplex networks and numerical experiments for all considered problems will be presented. -- Indico :: Email Notifier https://events.dm.unipi.it/e/329

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Colloquium Daniela Calvetti
by Silvia Gazzola 20 Oct '25

20 Oct '25

Cari tutte e tutti, Vi scrivo per segnalarvi che, la prossima settimana, Daniela Calvetti<https://mathstats.case.edu/faculty/daniela-calvetti/> sarà in visita presso il nostro dipartimento. In particolare, lunedì 27 ottobre, alle ore 16, presso l'Aula Magna del Dipartimento di Matematica, terrà un colloquium dal titolo: `Linear algebra joins probability in the search for sparse and group sparse solutions with few data’. Trovate ulteriori dettagli al link: https://www.dm.unipi.it/en/seminar/?id=68f20c6cdefecee83efcca3e Fatemi pur anche sapere se desiderate interagire con Daniela Calvetti intanto che si trova a Pisa. Cordiali saluti, Silvia ============= Dr Silvia Gazzola Dipartimento di Matematica Università di Pisa https://sites.google.com/view/silviaspersonalwebpage/silvias-homepage ---------------------------------------------------------------------------------------------------------------------------------------------------------- You may receive this email outside my normal working hours — no response is expected outside your working hours ----------------------------------------------------------------------------------------------------------------------------------------------------------

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Seminario Fabio Credali - 25 Settembre 2025 - ore 12.00
by Luca Heltai 17 Sep '25

17 Sep '25

Car* tutt*, vi scrivo per segnalare un seminario che si terrà il 25 Settembre alle ore 12.00 in Sala riunioni presso il dipartimento di Matematica: Speaker: Dr. Fabio Credali, King Abdullah University of Science and Technology - KAUST Title: Advances on the finite element discretization of fluid-structure interaction problems Abstract: We review the main features of an unfitted finite element method for fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. A coupling term describes the interaction between fluid and solid and it involves functions defined over two distinct non-matching grids, thus its evaluation is not trivial. We study the effect of exact and inexact integration by presenting quadrature estimates supported by numerical results. Moreover, we show that our method is stable even in presence of small cut cells and we provide an upper bound for the condition number. Finally, we outline the mass conservation properties of the proposed approach in the case of popular conforming finite element spaces. This work is a collaborative effort with Daniele Boffi, Lucia Gastaldi and Najwa Alshehri.

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Convegno al Centro De Giorgi: Morphogenesis and morphing, 200 years after Gauss
by Luca Heltai 15 Sep '25

15 Sep '25

Cari tutti, vi giro le informazioni su un convegno molto interessante giratemi da Antonio De Simone. La deadline per la registrazione è oggi... Cordialmente, Luca. > Begin forwarded message: > > From: Antonio De Simone <antonio.desimone(a)santannapisa.it> > Subject: [Junk released by User action] Convegno al Centro De Giorgi: Morphogenesis and morphing, 200 years after Gauss > Date: 10 September 2025 at 12:53:19 CEST > To: Alessandro Tognetti <alessandro.tognetti(a)unipi.it>, Roberto Paroni <rob.paroni(a)gmail.com>, Simone Camarri <simone.camarri(a)unipi.it>, "luca.heltai(a)unipi.it" <luca.heltai(a)unipi.it> > > Cari Roberto, Alessandro, Simone, Luca, > > il 20-24 ottobre prossimi organizzo un convegno internazionale al Centro De Giorgi della Scuola Normale Superiore, insieme ai matematici: > > https://indico.sns.it/event/122/ > https://indico.sns.it/event/122/ > > Sarà un convegno di alto livello, molto interdisciplinare e penso che potrebbe essere interessante per molti ricercatori e studenti a UniPI. > Posso chiedervi la cortesia di diffondere questa informazione attraverso i canali della vostra università e dei vostri dipartimenti? > Occorre registrarsi alla pagina web qui sotto: > > https://indico.sns.it/event/122/registrations/69/ > > Ovviamente siete invitantissimi a partecipare. > Grazie mille e cari saluti, > Antonio > > *** English Version*** > International worship at Centro De Giorgi, Pisa > 20-24 October 2025 > Morphogenesis and morphing, 200 years after Gauss: > > On October 20-24 there will be an interesting and high level international workshop at Centro De Giorgi (Scuola Normale Superiore, Pisa) entitled: > Morphogenesis and morphing, 200 years after Gauss: > > https://indico.sns.it/event/122/ > > Registration is required, via the following webpage: > > https://indico.sns.it/event/122/registrations/69/ > > Thank you and best wishes, > Antonio DeSimone > ****

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posizione dottorato Aalto university
by Federico Poloni 01 Jul '25

01 Jul '25

Cari tutti, Vanni Noferini mi segnala questa posizione di dottorato su “Matrix nearness problems via Riemannian optimisation’’: https://www.aalto.fi/en/open-positions/doctoral-candidate-in-applied-mathem… Inoltro qui, anche se è in concorrenza con le nostre a Pisa in Matematica e HPSC ( https://www.dm.unipi.it/bandi-di-concorso-per-lammissione-ai-dottorati-di-r… ). Un caro saluto, Federico -- --Federico Poloni Dipartimento di Informatica, Università di Pisa https://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Nello Cristianini a Pisa
by Gianna M. Del Corso 20 May '25

20 May '25

Cari colleghi, Giovedì 22/5 alle 11:00 nell’aula magna dell’ex facoltà di Scienze, Nello Cristianini, professore di intelligenza artificiale all’ Università di Bath terrà una presentazione del suo libro "Machina Sapiens <https://www.mulino.it/isbn/9788815384461>” discutendo dei rischi e delle implicazioni dell'AI generativa. Sarà un'ottima occasione per approfondire temi di grande attualità nel nostro campo con uno dei principali esperti dell'argomento, che li presenterà in modo accessibile. Vi incoraggio a partecipare e a contribuire alla discussione, invitando anche gli studenti del nostro corso di laurea. Cordiali saluti, Gianna @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@

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[Indico] Federica Mugnaioni, Optimal and Scalable Augmented Lagrangian preconditioners for Fictitious Domain problems, 13/05/2025, 11:00 Europe/Rome
by fabio.durastante＠unipi.it 12 May '25

12 May '25

Title: Optimal and Scalable Augmented Lagrangian preconditioners for Fictitious Domain problems, Speaker(s): Federica Mugnaioni, Scuola Normale Superiore, Date and time: 13 May 2025, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Saletta Riunioni). You can access the full event here: https://events.dm.unipi.it/e/321 Abstract -------- One of the major drawbacks of using Fictitious Domain methods is the computational demands of solving the associated large-scale linear systems, both in terms of time and memory. To address this issue, we propose two augmented Lagrangian-based preconditioners for efficiently solving linear systems of equations with a block two-by-two and three-by-three structure arising from fictitious domain problems and from finite element discretizations of immersed boundary methods. We consider two relevant examples to illustrate the performance of these preconditioners when used in conjunction with flexible GMRES: the Poisson and the Stokes fictitious domain problems. We provide a detailed spectral analysis, deriving lower and upper bounds for the eigenvalues of the preconditioned matrix and showing their independence with respect to discretization parameters. Furthermore, we discuss the eigenvalue distribution when inexact versions of the preconditioners are employed. We show the effectiveness of the proposed approach and the robustness of our preconditioning strategies through extensive numerical tests in both two and three dimensions, using different immersed geometries.M. Benzi, M. Feder, L. Heltai and F. Mugnaioni. Optimal and Scalable Augmented Lagrangian preconditioners for Fictitious Domain problems. arXiv:2504.11339, 2025 Note ---- A reminder of tomorrow's seminar. -- Indico :: Email Notifier https://events.dm.unipi.it/e/321

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[Indico] Federica Mugnaioni, Optimal and Scalable Augmented Lagrangian preconditioners for Fictitious Domain problems, 13/05/2025, 11:00 Europe/Rome
by fabio.durastante＠unipi.it 28 Apr '25

28 Apr '25

Title: Optimal and Scalable Augmented Lagrangian preconditioners for Fictitious Domain problems, Speaker(s): Federica Mugnaioni, Scuola Normale Superiore, Date and time: 13 May 2025, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Saletta Riunioni). You can access the full event here: https://events.dm.unipi.it/e/321 Abstract -------- One of the major drawbacks of using Fictitious Domain methods is the computational demands of solving the associated large-scale linear systems, both in terms of time and memory. To address this issue, we propose two augmented Lagrangian-based preconditioners for efficiently solving linear systems of equations with a block two-by-two and three-by-three structure arising from fictitious domain problems and from finite element discretizations of immersed boundary methods. We consider two relevant examples to illustrate the performance of these preconditioners when used in conjunction with flexible GMRES: the Poisson and the Stokes fictitious domain problems. We provide a detailed spectral analysis, deriving lower and upper bounds for the eigenvalues of the preconditioned matrix and showing their independence with respect to discretization parameters. Furthermore, we discuss the eigenvalue distribution when inexact versions of the preconditioners are employed. We show the effectiveness of the proposed approach and the robustness of our preconditioning strategies through extensive numerical tests in both two and three dimensions, using different immersed geometries.M. Benzi, M. Feder, L. Heltai and F. Mugnaioni. Optimal and Scalable Augmented Lagrangian preconditioners for Fictitious Domain problems. arXiv:2504.11339, 2025 -- Indico :: Email Notifier https://events.dm.unipi.it/e/321

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Colloquium 17 aprile ore 16.00
by Stefano Massei 15 Apr '25

15 Apr '25

Cari tutti, a nome della Commissione Colloquia di Dipartimento, vi ricordo che giovedì 17 aprile alle 16.00 in AULA MAGNA Virginie Ehrlacher<https://team.inria.fr/matherials/team-members/virginie-ehrlacher-galland/> (Ecole des Ponts ParisTech) terrà un <https://www.dm.unipi.it/en/seminar/?id=67a64aff762f5b32f7b4dfd3> colloquium<https://www.dm.unipi.it/en/seminar/?id=67a64aff762f5b32f7b4dfd3> sul tema: “A sparse approximation of the Lieb functional with moment constraints”. Cordiali saluti, Stefano Massei

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Next NUMPI seminar: set the date
by Fabio Durastante 15 Apr '25

15 Apr '25

Good morning, We would like to fix the date for the next NUMPI seminar in May. It will be a seminar held by Federica Mugnaioni (Ph.D. Scuola Normale Superiore) on the topic of preconditioners for discretization of fictitious domain problems. Please reply with your availability for the days of May 12/13 and we will try to organize it at a time convenient for most of us: https://date.dm.unipi.it/Vh6AwjL3MKGWBESp Best, Fabio

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[Indico] Raf Vandebril, On inverse eigenvalue problems for multiple orthogonal polynomials, 14/04/2025, 11:30 Europe/Rome
by leonardo.robol＠unipi.it 14 Apr '25

14 Apr '25

Title: On inverse eigenvalue problems for multiple orthogonal polynomials, Speaker(s): Raf Vandebril, KU Leuven, Date and time: 14 Apr 2025, 11:30 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Saletta Riunioni). You can access the full event here: https://events.dm.unipi.it/e/318 Abstract -------- Multiple orthogonal polynomials (MOP's) arise in various applications, including approximation theory, random matrix theory, and numerical integration. To define MOP's, one needs multiple inner products, leading to two types of MOP’s, which are mutually biorthogonal. These MOP's satisfy recurrence relations, which can be linked to linear algebra, via discretization. As a result we get an inverse eigenvalue problem to retrieve the matrix of recurrences directly. We provide two algorithms for solving the inverse eigenvalue problem, one based on classical equivalence transformations and one linked to (block) Krylov methods. Numerical illustrations are provided to demonstrate correctness of the approach and also reveal the strong sensitivity of the problem. -- Indico :: Email Notifier https://events.dm.unipi.it/e/318

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[Indico] Raf Vandebril, On inverse eigenvalue problems for multiple orthogonal polynomials, 14/04/2025, 11:30 Europe/Rome
by leonardo.robol＠unipi.it 08 Apr '25

08 Apr '25

Title: On inverse eigenvalue problems for multiple orthogonal polynomials, Speaker(s): Raf Vandebril, KU Leuven, Date and time: 14 Apr 2025, 11:30 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Saletta Riunioni). You can access the full event here: https://events.dm.unipi.it/e/318 Abstract -------- Multiple orthogonal polynomials (MOP's) arise in various applications, including approximation theory, random matrix theory, and numerical integration. To define MOP's, one needs multiple inner products, leading to two types of MOP’s, which are mutually biorthogonal. These MOP's satisfy recurrence relations, which can be linked to linear algebra, via discretization. As a result we get an inverse eigenvalue problem to retrieve the matrix of recurrences directly. We provide two algorithms for solving the inverse eigenvalue problem, one based on classical equivalence transformations and one linked to (block) Krylov methods. Numerical illustrations are provided to demonstrate correctness of the approach and also reveal the strong sensitivity of the problem. -- Indico :: Email Notifier https://events.dm.unipi.it/e/318

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[Indico] Prof. Michiel Hochstenbach, Recent Progress in Steplengths in Gradient Methods for Unconstrained Optimization, 3/27/25, 2:00 PM Europe/Rome
by stefano.massei＠unipi.it 26 Mar '25

26 Mar '25

Title: Recent Progress in Steplengths in Gradient Methods for Unconstrained Optimization, Speaker(s): Prof. Michiel Hochstenbach, Eindhoven University of Technology, Date and time: Mar 27, 2025, 2:00 PM (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di matematica (Aula riunioni). You can access the full event here: https://events.dm.unipi.it/e/314 Abstract -------- We review recent progress in stepsizes in gradient methods for unconstrained numerical optimization, for both quadratic and general nonlinear problems, including several very valuable contributions from Italian experts such as Prof. Zanni and colleagues. We will review Barzilai-Borwein steps and secant equations, and show developments in harmonic stepsizes and homogeneous secant equations. The key idea is that the steplength is selected as the inverse Ritz value of an average Hessian. For limited memory methods, we will address several challenges, including how to avoid negative or non-real stepsize candidates. We will also present some open problems. This talk reflects joint work with Giulia Ferrandi. -- Indico :: Email Notifier https://events.dm.unipi.it/e/314

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Discussione tesi di dottorato di Alberto Bucci
by Leonardo Robol 21 Feb '25

21 Feb '25

Cari tutti e tutte, lunedì 24/02, alle 10.00, Alberto Bucci discuterà la sua tesi di dottorato in Aula Magna del Dipartimento di Matematica. Il titolo della tesi è "Randomized techniques for low-rank approximation of matrices and tensors with applications". Chiunque volesse partecipare è benvenuto/a! A presto, -- Leonardo.

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Online seminar at University of Rome "Tor Vergata": Stefano Pozza: 6 febbraio alle 12:30
by Fabio Durastante 29 Jan '25

29 Jan '25

Dear everybody, Forwarding of a NA seminar announcement that can also be followed online at the University of Rome "Tor Vergata". Best, Fabio ________________________________ Da: Mariarosa Mazza <mariarosa.mazza(a)uniroma2.it> Inviato: mercoledì 29 gennaio 2025 18:49 A: mariarosa.mazza(a)uniroma2.it Oggetto: seminario Pozza: 6 febbraio alle 12:30 Car* tutt*, giovedi 6 febbraio alle 12.30 in aula Dal Passo, Dipartimento di Matematica, Roma Tor Vergata, il Dott. Stefano Pozza (Charles University) terrà un seminario dal titolo (abstract in calce): "How to express the solution of an ODE as a linear system (in a suitable algebra) and exploit it for fast computation and network analysis". Il seminario può essere seguito online usando il link: https://teams.microsoft.com/l/meetup-join/19%3ad48916dee7364e0bbb08216ea621… Vi prego di diffondere l'annuncio fra i possibili interessati. Un caro saluto e grazie, Mariarosa --------------------------------------- Abstract: The solution of systems of non-autonomous linear ordinary differential equations is crucial in various applications, such as nuclear magnetic resonance spectroscopy. We introduced a new solution expression in terms of a generalization of the Volterra composition. Such an expression is linear in a particular algebraic structure of distributions, which can be mapped onto a subalgebra of infinite matrices. It is possible to exploit the new expression to devise fast numerical methods for linear non-autonomous ODEs. As a first example, we present a new method for the operator solution of the generalized Rosen-Zener model, a system of linear non-autonomous ODEs from quantum mechanics. The new method’s computing time scales linearly with the model’s size in the numerical experiments. A second example is the analysis of temporal network, where the new expression might lead to novel extension of subgraph centrality indexes. -- ------------------------------------- Dr. Mariarosa Mazza University of Rome Tor Vergata Via della Ricerca Scientifica, 1 00133, Rome, Italy Email: mariarosa.mazza(a)uniroma2.it<mailto:mariarosa.mazza@uniroma2.it> Tel: 0039 06-7259-4636 Url: https://sites.google.com/site/mariarosamazza1/ ---------------------------------

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Online Seminar: Peter Taylor, "The Role of Physical Understanding in Matrix-Analytic Methods"
by Federico Poloni 14 Jan '25

14 Jan '25

In case someone is interested, let me share this online event. A flyer is attached. Speaker: Professor Peter Taylor, The University of Melbourne Date: Thursday, February 6 2025 Time: 22:00 Italian time (!!) Title: The Role of Physical Understanding in Matrix-Analytic Methods Abstract: Since Marcel Neuts first showed that Markov chains of GI/M/1 type have a matrix-geometric stationary distribution in the 1970s and 1980s, the interplay between analytic properties and physical interpretation has played a major part in the development of matrix-analytic methods for stochastic models. Most performance measures of interest in such models can be expressed in terms of the solutions of equations involving matrix power series, which have to be solved numerically. Over the years, various iterative algorithms have been proposed for doing this. In order to establish convergence, and gain information about the speed of convergence, it is often helpful to think about the physical interpretation of the iterates. I shall discuss the physical interpretation of matrix-analytic algorithms that have been proposed for analysing block-structured Markov additive models. -- --Federico Poloni Dipartimento di Informatica, Università di Pisa https://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Lauri Nyman, "Riemann-Oracle: A framework for matrix nearness problems" 10/12/2024, 16:00
by Federico Poloni 10 Dec '24

10 Dec '24

The following seminar will take place next week; Lauri Nyman and Vanni Noferini from Aalto University are visiting the department of computer science in that week. Title: Riemann-Oracle: A framework for matrix nearness problems Speaker: Lauri Nyman, Aalto University, Espoo, Finland Where: Sala Seminari Est, Dipartimento di Informatica When: Tuesday December 10, 2024; 16:00 Abstract: In this talk, we propose a versatile approach for addressing a large family of matrix nearness problems. In these problems, the task is to find a matrix nearest to a given one that satisfies a desired constraint. The method is based on splitting a matrix nearness problem into two nested optimization problems, of which the inner one can be solved cheaply and exactly, while the outer one can be recast as an unconstrained optimization task over a smooth real Riemannian manifold. We also show that the objective function to be minimized on the Riemannian manifold can be discontinuous, thus requiring regularization techniques, and we give conditions for this to happen. Finally, we demonstrate the practical applicability of our method by implementing it for a number of matrix nearness problems that are relevant for applications, including nearest singular matrix with a given sparsity structure, nearest singular matrix polynomial, approximate GCD and nearest unstable matrix. -- --Federico Poloni Dipartimento di Informatica, Università di Pisa https://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Short-term Research Associate position @ University of Pisa -- dealii-X project
by Luca Heltai 09 Dec '24

09 Dec '24

Dear all, please share the following information with possible candidates, and to colleagues that may know of possible candidates. Thanks! Luca. Numerical Analysis Group @ University of Pisa Start Date: March 1st Application Deadline: January 24th Application Portal: <https://bandi.unipi.it/public/Bandi/Detail/150eaadb-8fec-4fc5-acb6-593dc7a2…> The University of Pisa invites applications for a short-term Research Associate position within the dealii-X project. This role, based in the Department of Mathematics, will concentrate on Numerical Analysis and the creation of advanced numerical tools for high-performance simulations using the deal.II library. The dealii-X project aims to create an Exascale Framework for Digital Twins of the Human Body. This initiative seeks to enhance personalized medicine through sophisticated computational models, enabling scalable and detailed simulations of human organs. We are looking for dynamic individuals with a strong scientific CV relevant to numerical analysis and simulations (a Master degree in a scientific subject is mandatory, a PhD is a plus). The successful candidate will work on the development and optimization of numerical tools for high-performance simulations in the deal.II library, focusing on meshing techniques, advanced coupling methods, non-matching techniques, reduced order methods, and large scale preconditioning techniques. The role will involve a tight collaboration with other international teams and team members, contributing to the development of the deal.II library. Key information: - Research Focus: Development and optimization of numerical tools for high-performance simulations in the deal.II library - Department of Mathematics, University of Pisa - Numerical Analysis and High Performance Scientific Computing - Contract Duration: 24 months - Gross Annual Salary: €32,427.96 - Application Deadline: 24th January 2025 - Starting Date: 1st March 2025 or as soon as possible thereafter

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Due Giorni di Algebra Lineare Numerica e Applicazioni @ UNIPI 20/21 January 2025 (Reminder)
by Fabio Durastante 25 Nov '24

25 Nov '24

A friendly reminder that registration for the /20th Due Giorni di Algebra Lineare Numerica e Applicazioni/ (January 20-21, 2025, at the University of Pisa) will close on *November 30, 2024*. This is the 20th workshop in a series dedicated to Numerical Linear Algebra and Applications. It aims at gathering the Italian Numerical Linear Algebra scientific community to discuss recent advances in this area and to promote the exchange of novel ideas and collaboration among researchers. We strongly encourage contributions by junior scholars on theoretical and computational topics, as well as on applications. Contributions covering other areas requiring tools from Numerical Linear Algebra are very welcome. Topics of interest include (but are not limited to): iterative methods for large-scale linear systems, preconditioning, eigen and singular values, numerical optimization, numerical dynamical systems, mathematics of machine learning, structured matrices, tensors, matrix functions, Krylov methods, randomized linear algebra algorithms, and high-performance computing for matrix computations. Applications include optimization and control, image processing and inverse problems, networks and graphs, machine learning and artificial neural networks, uncertainty quantification, finance, material sciences, life sciences, and industrial processes. Steering committee: M. Benzi, M. Donatelli, N. Guglielmi, B. Meini, V. Simoncini Important dates: - Registration is open with Deadline 30 Nov 2024 - Call for Abstracts is open with Deadline 30 Nov 2024 Location: - Area Bruno Pontecorvo of the University of Pisa The conference is without registration fee, but registration is mandatory. There is a limited amount of support for PhD students who want to attend the event, application can be done through the registration form. Full information are available at the web-page: https://events.dm.unipi.it/event/280/ The organizing committee, P. Boito, G.M. Del Corso, F. Durastante, S. Gazzola, L. Heltai, S. Massei, C. Pagliantini, F. Poloni, L. Robol.

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"Matematici a Lavoro" Seminar: From the America's Cup to the quantum realm: a math journey - N. Giuliani (Applied Materials)
by Fabio Durastante 06 Nov '24

06 Nov '24

Hi everybody, This is a seminar for the series /Matematici a Lavoro/ ("Mathematicians at Work") organized by the Department of Mathematics and whose speakers are scientists who work outside of the university world and who discuss how mathematics intersects with their work. They are mainly aimed at master's and doctoral students, but given the topic, it may be of wider interest. -- Fabio* * *Title:* From the America's Cup to the quantum realm: a math journey *Speaker: *Nicola Giuliani (Applied Materials) *Date and Time:* Tuesday, Nov 12, 2024 18:00 — 19:00 Aula Magna (Department of Mathematics) *Abstract: *In this seminar I will talk about my work experience. I will explain what inspired me to become an aeronautical engineer and a numerical analyst. Quite interestingly my work has always evolved to study increasingly smaller things. My academic research started with the study of ships (meters) and then It focused on the study of microswimmers (micrometers). In the last five years I worked at Applied Materials developing a software to predict the performance of nanoelectronics devices (some nanometers) where quantum effects can play an important role. *Info:* https://www.dm.unipi.it/en/seminar/?id=672b7f157a42a9b2643d0ca3

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[Indico] Prof. Andreas Frommer, Structure-aware Krylov approximations to generalized Cayley transforms, 25/10/2024, 11:00 Europe/Rome
by fabio.durastante＠unipi.it 23 Oct '24

23 Oct '24

Title: Structure-aware Krylov approximations to generalized Cayley transforms, Speaker(s): Prof. Andreas Frommer, University of Wuppertal, Date and time: 25 Oct 2024, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Scuola Normale Superiore (Aula Mancini). You can access the full event here: https://events.dm.unipi.it/e/296 Abstract -------- Generalized Cayley transforms arise in implicit numerical integration schemes for ordinary differential equations and differential-algebraic equations. We consider Arnoldi-type methods to approximate the action of such a Cayley transform on a vector and investigate how energy conservation or dissipation can be enforced at the level of each Arnoldi iterate, not just at the level of the exact solution. We also investigate generalizations to higher order collocation methods. Note ---- Reminder of tomorrow's seminar -- Indico :: Email Notifier https://events.dm.unipi.it/e/296

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Difesa dottorato - PhD defense
by Igor SIMUNEC 18 Oct '24

18 Oct '24

Cari tutti, Venerdì 25 ottobre alle 14.30 difenderò la mia tesi di dottorato, intitolata "Advances in polynomial and rational Krylov methods for matrix functions with applications", in Aula Bianchi Lettere (Scuola Normale Superiore). Dopo la difesa ci sarà un piccolo brindisi e rinfresco nel chiostro del Palazzo della Carovana. Chiunque volesse partecipare, o anche soltanto passare per un saluto, è benvenuto! A presto, Igor --- Dear all, On October 25th at 14.30 I will defend my PhD thesis, titled "Advances in polynomial and rational Krylov methods for matrix functions with applications", in Aula Bianchi Lettere (Scuola Normale Superiore). After the defense there will be some refreshments in the internal courtyard of the Palazzo della Carovana. You are all welcome to participate! Best, Igor

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[Indico] Prof. Andreas Frommer, Structure-aware Krylov approximations to generalized Cayley transforms, 10/25/24, 11:00 AM Europe/Rome
by fabio.durastante＠unipi.it 17 Oct '24

17 Oct '24

Title: Structure-aware Krylov approximations to generalized Cayley transforms, Speaker(s): Prof. Andreas Frommer, University of Wuppertal, Date and time: Oct 25, 2024, 11:00 AM (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Scuola Normale Superiore (Aula Mancini). You can access the full event here: https://events.dm.unipi.it/e/296 Abstract -------- Generalized Cayley transforms arise in implicit numerical integration schemes for ordinary differential equations and differential-algebraic equations. We consider Arnoldi-type methods to approximate the action of such a Cayley transform on a vector and investigate how energy conservation or dissipation can be enforced at the level of each Arnoldi iterate, not just at the level of the exact solution. We also investigate generalizations to higher order collocation methods. -- Indico :: Email Notifier https://events.dm.unipi.it/e/296

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Seminar announcement: A finite element approximation of a simplified model for smart fluids: an error analysis 9/10
by Fabio Durastante 08 Oct '24

08 Oct '24

Good morning, Colleagues in the Analysis section have organized this seminar by Alex Kaltenbach that may be of interest to some of us. The detailed information follows. Best, Fabio Speaker: Alex Kaltenbach, Technische Universität Berlin Seminar: A finite element approximation of a simplified model for smart fluids: an error analysis Date: October 9th at 5:00 pm, Aula Riunioni (Maths Department) Abstract: In this talk, a finite element approximation of the steady $p(\cdot)$-Navier--Stokes equations ($p(\cdot)$ is variable dependent) is examined for orders of convergence by assuming natural fractional regularity assumptions on the velocity vector field and the kinematic pressure. Numerical experiments confirm the quasi-optimality of the \textit{a priori} error estimates (for the velocity). The steady $p(\cdot)$-Navier--Stokes equations are a prototypical example of a non-linear system with variable growth conditions. They appear naturally in physical models for so-called \textit{smart fluids}, \textit{e.g.}, electro-rheological fluids, micro-polar electro-rheological fluids, magneto-rheological fluids, chemically reacting fluids, and thermo-rheological fluids, and have the potential for an application in numerous areas, \textit{e.g.}, in electronic, automobile, heavy machinery, military, and biomedical industry.

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[Indico] Mehdi Najafi Kalyani, A two-dimensional minimum residual technique for accelerating two-step iterative solvers, 04/10/2024, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 02 Oct '24

02 Oct '24

Title: A two-dimensional minimum residual technique for accelerating two-step iterative solvers, Speaker(s): Mehdi Najafi Kalyani, University of Pisa, Date and time: 4 Oct 2024, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). You can access the full event here: https://events.dm.unipi.it/e/289 Abstract -------- In this talk, we present a technique to speed up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each sub-iterate is minimized over a certain two-dimensional subspace. Convergence properties of the resulting method will be discussed in detail. It will be further shown that the approach can be developed to solve (regularized) normal equations arising from the discretization of ill-posed problems. Numerical experiments will be disclosed to illustrate the performance of exact and inexact variants of the method for some test problems. -- Indico :: Email Notifier https://events.dm.unipi.it/e/289

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[Indico] Mehdi Najafi Kalyani, A two-dimensional minimum residual technique for accelerating two-step iterative solvers, 04/10/2024, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 18 Sep '24

18 Sep '24

Title: A two-dimensional minimum residual technique for accelerating two-step iterative solvers, Speaker(s): Mehdi Najafi Kalyani, University of Pisa, Date and time: 4 Oct 2024, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). You can access the full event here: https://events.dm.unipi.it/e/289 Abstract -------- In this talk, we present a technique to speed up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each sub-iterate is minimized over a certain two-dimensional subspace. Convergence properties of the resulting method will be discussed in detail. It will be further shown that the approach can be developed to solve (regularized) normal equations arising from the discretization of ill-posed problems. Numerical experiments will be disclosed to illustrate the performance of exact and inexact variants of the method for some test problems. -- Indico :: Email Notifier https://events.dm.unipi.it/e/289

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Seminar on Quantum Computing: Andrew Daley (University of Oxford, UK) Monday 23/09/2024
by Gianna M. Del Corso 18 Sep '24

18 Sep '24

Dear All, As part of the CN1-SPOKE 10 on Quantum Computing, this year too we plan to organize a weekly seminar series. The first event this year is a talk proposed by by Marilu Chiofalo and Jorge Yago Malo. Title: Analogue and digital quantum simulation: state of the art and opportunities Speaker: Andrew Daley (University of Oxford, UK) Venue: Sala Galilei (room 131, Bldg. C, Department of Physics) Time: Monday, 23/09/2024, 15:00 Abstract: There has been impressive recent progress in developing highly controlled quantum systems, ranging from superconducting qubits to neutral atoms in tweezer arrays. These systems provide a route to medium-scale quantum computing, but also the possibility to build and study models of many-body systems. These range from electrons in solid state physics and materials across to toy models for information spreading in black holes (made possible by long-range interactions). This impressive progress had led to new opportunities for studying basic science, but has also opened pathways towards making quantum simulation useful in solving problems from chemistry, materials and wider fields. I will give an introduction to the state of the art in these systems, illustrated with our recent theoretical work on fast scrambling of quantum information in systems with long-range interactions. I will also discuss the opportunities and challenges associated with important questions, including (1) To which degree can analogue devices be quantitatively reliable? And (2) when can we use these systems to give us access to useful information that we cannot compute with conventional supercomputers? Everyone is welcome! @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@

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Upcoming workshop: NumPI day
by Stefano Massei 18 Sep '24

18 Sep '24

Dear all, I am glad to announce to you that Monday 23rd September we will have a one-day workshop of numerical analysis titled NumPI day. Anyone interested is welcome! The event will take place from 9 a.m. to 16 p.m. in the Aula Magna of the department of Mathematics, see the attached schedule. Best regards, Stefano

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[Indico] Dr Maria Strazzullo, Nonlinear Feedback Control via Dynamical Low-Rank Approximation, 09/09/2024, 15:30 Europe/Rome
by noreply＠cs.dm.unipi.it 09 Sep '24

09 Sep '24

Title: Nonlinear Feedback Control via Dynamical Low-Rank Approximation, Speaker(s): Dr Maria Strazzullo, Politecnico di Torino, Date and time: 9 Sept 2024, 15:30 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento Di Matematica (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/288 Abstract -------- Feedback control plays a crucial role in optimizing the performance of dynamical systems by minimizing a predefined cost functional, to stabilize the system towards a desired state. Despite its undeniable effectiveness, the applicability of feedback control is often limited by the high dimensionality of state spaces, a challenge that is even more pronounced in parametric settings. To overcome these limitations, we employ the Dynamical Low-Rank Approximation (DLRA) methodology, which offers an efficient and accurate solution to high-dimensional feedback control problems. Our approach significantly accelerates the solution of State-Dependent Riccati Equations (SDREs) for infinite horizon optimal control by providing a compact, low-dimensional representation of the system that evolves dynamically with respect to the problem. This not only enhances accuracy but also provides effective real-time control, solving several parametric instances simultaneously. To further accelerate the solution of the SDREs, we propose cascade-control (cc-) algorithms that leverage the Riccati solution from a previous parameter to improve the convergence of Newton-based methods applied to SDREs. The robustness and efficiency of our algorithms are validated through nonlinear test cases. Comparative analysis demonstrates that the proposed ccDLRA outperforms global Proper Orthogonal Decomposition model order reduction (ccPOD), offering superior speed and accuracy when compared to the full-order model (ccFOM) solution. Note ---- Reminder for this afternoon's seminar. -- Indico :: Email Notifier https://events.dm.unipi.it/e/288

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[Indico] Dr Maria Strazzullo, Nonlinear Feedback Control via Dynamical Low-Rank Approximation, 09/09/2024, 15:30 Europe/Rome
by fabio.durastante＠unipi.it 05 Sep '24

05 Sep '24

Title: Nonlinear Feedback Control via Dynamical Low-Rank Approximation, Speaker(s): Dr Maria Strazzullo, Politecnico di Torino, Date and time: 9 Sept 2024, 15:30 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento Di Matematica (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/288 Abstract -------- Feedback control plays a crucial role in optimizing the performance of dynamical systems by minimizing a predefined cost functional, to stabilize the system towards a desired state. Despite its undeniable effectiveness, the applicability of feedback control is often limited by the high dimensionality of state spaces, a challenge that is even more pronounced in parametric settings. To overcome these limitations, we employ the Dynamical Low-Rank Approximation (DLRA) methodology, which offers an efficient and accurate solution to high-dimensional feedback control problems. Our approach significantly accelerates the solution of State-Dependent Riccati Equations (SDREs) for infinite horizon optimal control by providing a compact, low-dimensional representation of the system that evolves dynamically with respect to the problem. This not only enhances accuracy but also provides effective real-time control, solving several parametric instances simultaneously. To further accelerate the solution of the SDREs, we propose cascade-control (cc-) algorithms that leverage the Riccati solution from a previous parameter to improve the convergence of Newton-based methods applied to SDREs. The robustness and efficiency of our algorithms are validated through nonlinear test cases. Comparative analysis demonstrates that the proposed ccDLRA outperforms global Proper Orthogonal Decomposition model order reduction (ccPOD), offering superior speed and accuracy when compared to the full-order model (ccFOM) solution. -- Indico :: Email Notifier https://events.dm.unipi.it/e/288

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Seminario a Settembre
by Luca SALUZZI 03 Aug '24

03 Aug '24

Cari tutti, vi mando questa email perche' a Settembre, la settimana del 9-13, verra' in visita Maria Strazzullo dal Politecnico di Torino e vorrei organizzare un suo seminario. Si pensava di farlo o Lunedì 9 o Martedi' 10. Voi avete preferenze su data e orario? Così da permettere di massimizzare il numero di partecipanti. Intanto buone vacanze e ci si vede a Settembre!! Ciao, Luca

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23/07/2024 — R. Van Beeumen — Seminari CN1-SPOKE 10 (Quantum Computing)
by Gianna M. Del Corso 23 Jul '24

23 Jul '24

Dear all, This is a reminder for today’s seminar on quantum computing. Title: Hybrid Quantum-Classical Krylov Methods for Eigenvalue Computation Speaker: Roel Van Beeumen (Lawrence Berkeley National Laboratory) Venue: Sala Gerace, Dipartimento di Informatica Time: Tuesday, 23/07/2024, 14:30 Below the link for the online attendance. https://teams.microsoft.com/l/meetup-join/19%3ameeting_MjliOWRmMDAtMjA4ZC00… Everyone is welcome to attend! Gianna @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@

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Seminar on Quantum Computing: Roel Van Beeumen Tuesday 23/7, 14:30
by Gianna M. Del Corso 16 Jul '24

16 Jul '24

Dear All, As part of the CN1-SPOKE 10 on Quantum Computing, we are pleased to announce the last seminar before the summer break. Title: Hybrid Quantum-Classical Krylov Methods for Eigenvalue Computation Speaker: Roel Van Beeumen (Lawrence Berkeley National Laboratory) Venue: Sala Gerace, Dipartimento di Informatica Time: Tuesday, 23/07/2024, 14:30 Abstract: Classical algorithms based on Krylov subspaces are among the most successful tools in the field of numerical linear algebra. More recently, the emergence of quantum subspace methods has resulted in a promising class of hybrid quantum-classical algorithms for eigenvalue approximation, e.g., in the fields of condensed matter physics and electronic structure theory. These quantum Krylov methods harness quantum computers to generate the subspace basis states and retrieve the projected problem through quantum measurement. However, the classical computation of the Ritz values often poses challenges due to the ill-conditioning of the associated generalized eigenvalue problem. In this talk, we present an overview of quantum subspace algorithms from a numerical linear algebra perspective. We discuss strategies to avoid solving an ill-conditioned eigenvalue problem, explain their implementation on quantum computers, and provide numerical and theoretical evidence of their convergence. Furthermore, we present strategies to improve the robustness, especially in the presence of noise. Everyone is welcome to attend! Gianna @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@

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[Indico] Dr Jie Meng, Theoretical and computational properties of quasi-Toeplitz M-matrices, 15/07/2024, 15:00 Europe/Rome
by fabio.durastante＠unipi.it 14 Jul '24

14 Jul '24

Title: Theoretical and computational properties of quasi-Toeplitz M-matrices, Speaker(s): Dr Jie Meng, Ocean University of China, Date and time: 15 Jul 2024, 15:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/287 Abstract -------- A quasi-Toeplitz matrix is a semi-infinite matrix of the form $A=T(a)+E$, where $T(a)$ is a Toeplitz matrix with entries $(T(a))_{i,j}=a_{j-i}$, for $a_{j-i}\in\mathbb C$, $i,j\ge 1$ and $E$ is a compact correction. Quasi-Toeplitz $M$-matrices are encountered in the study of quadratic matrix equations arising in the analysis of a 2-dimensional Quasi-Birth-Death (QBD) stochastic process. We investigate the properties of such matrices and provide conditions under which a quasi-Toeplitz matrix is an $M$-matrix. We show that under a mild and easy-to-check condition, an invertible quasi-Toeplitz $M$-matrix has a unique square root that is an $M$-matrix possessing quasi-Toeplitz structure. Some issues concerning the computation of the square root of quasi-Toeplitz $M$-matrices are discussed and numerical experiments are performed -- Indico :: Email Notifier https://events.dm.unipi.it/e/287

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Difesa dottorato
by Angelo Alberto CASULLI 12 Jul '24

12 Jul '24

Cari tutti, Lunedì 22 luglio alle 14.30 discuterò la mia tesi di dottorato dal titolo "Block rational Krylov methods for matrix equations and matrix functions" presso la Scuola Normale. Chiunque abbia piacere di partecipare è il benvenuto! Seguirà un piccolo rinfresco nel chiostro della Scuola. A presto, Angelo Casulli

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[Indico] Dr Jie Meng, Theoretical and computational properties of quasi-Toeplitz M-matrices, 7/15/24, 3:00 PM Europe/Rome
by fabio.durastante＠unipi.it 04 Jul '24

04 Jul '24

Title: Theoretical and computational properties of quasi-Toeplitz M-matrices, Speaker(s): Dr Jie Meng, Ocean University of China, Date and time: Jul 15, 2024, 3:00 PM (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/287 Abstract -------- A quasi-Toeplitz matrix is a semi-infinite matrix of the form $A=T(a)+E$, where $T(a)$ is a Toeplitz matrix with entries $(T(a))_{i,j}=a_{j-i}$, for $a_{j-i}\in\mathbb C$, $i,j\ge 1$ and $E$ is a compact correction. Quasi-Toeplitz $M$-matrices are encountered in the study of quadratic matrix equations arising in the analysis of a 2-dimensional Quasi-Birth-Death (QBD) stochastic process. We investigate the properties of such matrices and provide conditions under which a quasi-Toeplitz matrix is an $M$-matrix. We show that under a mild and easy-to-check condition, an invertible quasi-Toeplitz $M$-matrix has a unique square root that is an $M$-matrix possessing quasi-Toeplitz structure. Some issues concerning the computation of the square root of quasi-Toeplitz $M$-matrices are discussed and numerical experiments are performed -- Indico :: Email Notifier https://events.dm.unipi.it/e/287

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[Indico] Taejun Park, A low-rank approximation of parameter-dependent matrices via CUR decomposition, 13/06/2024, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 11 Jun '24

11 Jun '24

Title: A low-rank approximation of parameter-dependent matrices via CUR decomposition, Speaker(s): Taejun Park, University of Oxford, Date and time: 13 Jun 2024, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/285 Abstract -------- Finding a low-rank approximation for parameter-dependent matrices $A(t)$ is an important task appearing in dynamical systems and image series compression. In this talk, we present an efficient randomized algorithm that computes a low-rank approximation of $A(t)$ at finite specified parameter values using the CUR decomposition. The key idea lies in reusing the same or a similar set of column and row indices for the CUR decomposition at nearby parameter values. The resulting algorithm is rank-adaptive, certifiable and has complexity that compares favorably to existing methods. This is joint work with Yuji Nakatsukasa. -- Indico :: Email Notifier https://events.dm.unipi.it/e/285

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Fwd: seminario Pearson: 6 giugno alle 14:30
by Fabio Durastante 31 May '24

31 May '24

Buonasera, Inoltro il seguente annuncio di seminario. Saluti, Fabio -------- Messaggio Inoltrato -------- Oggetto: seminario Pearson: 6 giugno alle 14:30 Data: Wed, 29 May 2024 12:12:19 +0200 Mittente: Mariarosa Mazza <mariarosa.mazza(a)uniroma2.it> A: mariarosa.mazza(a)uniroma2.it Car* tutt*, giovedi 6 giugno alle 14.30 in aula Dal Passo, Dipartimento di Matematica, Roma Tor Vergata, il Prof. John Pearson (University of Edinburgh) terrà un seminario dal titolo: "Recent Developments in the Numerical Solution of PDE-Constrained Optimization Problems". Il seminario può essere seguito online usando il link: https://teams.microsoft.com/l/meetup-join/19%3ad48916dee7364e0bbb08216ea621… Vi prego di diffondere l'annuncio fra i possibili interessati. Grazie, Mariarosa ----------------------------------------------- ABSTRACT: Optimization problems subject to PDE constraints form a mathematical tool that can be applied to a wide range of scientific processes, including fluid flow control, medical imaging, option pricing, biological and chemical processes, and electromagnetic inverse problems, to name a few. These problems involve minimizing some function arising from a particular physical objective, while at the same time obeying a system of PDEs which describe the process. It is necessary to obtain accurate solutions to such problems within a reasonable CPU time, in particular for time-dependent problems, for which the “all-at-once” solution can lead to extremely large linear systems. In this talk we consider iterative methods, in particular Krylov subspace methods, to solve such systems, accelerated by fast and robust preconditioning strategies. In particular, we will survey several new developments, including block preconditioners for fluid flow control problems, a circulant preconditioning framework for solving certain optimization problems constrained by fractional differential equations, and multiple saddle-point preconditioners for block tridiagonal linear systems. We will illustrate the benefit of using these new approaches through a range of numerical experiments. This talk is based on work with Santolo Leveque (Scuola Normale Superiore, Pisa), Spyros Pougkakiotis (Yale University), Jacek Gondzio (University of Edinburgh), and Andreas Potschka (TU Clausthal). This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006). -- ------------------------------------- Dr. Mariarosa Mazza University of Rome Tor Vergata Via della Ricerca Scientifica, 1 00133, Rome, Italy Email:mariarosa.mazza@uniroma2.it Tel: 0039 06-7259-4636 Url:https://sites.google.com/site/mariarosamazza1/ ---------------------------------

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Due Giorni di Algebra Lineare Numerica e Applicazioni @ UNIPI 20/21 January 2025
by Fabio Durastante 31 May '24

31 May '24

We are pleased to announce the next edition of the Due Giorni di Algebra Lineare Numerica e Applicazioni @ UNIPI 20/21 January 2025 This is the 20th workshop in a series dedicated to Numerical Linear Algebra and Applications. It aims at gathering the Italian Numerical Linear Algebra scientific community to discuss recent advances in this area and to promote the exchange of novel ideas and collaboration among researchers. We strongly encourage contributions by junior scholars on theoretical and computational topics, as well as on applications. Contributions covering other areas requiring tools from Numerical Linear Algebra are very welcome. Topics of interest include (but are not limited to): iterative methods for large-scale linear systems, preconditioning, eigen and singular values, numerical optimization, numerical dynamical systems, mathematics of machine learning, structured matrices, tensors, matrix functions, Krylov methods, randomized linear algebra algorithms, and high-performance computing for matrix computations. Applications include optimization and control, image processing and inverse problems, networks and graphs, machine learning and artificial neural networks, uncertainty quantification, finance, material sciences, life sciences, and industrial processes. Steering committee: M. Benzi, M. Donatelli, N. Guglielmi, B. Meini, V. Simoncini Important dates: - Registration is open with Deadline 30 Nov 2024 - Call for Abstracts is open with Deadline 30 Nov 2024 Location: - Area Bruno Pontecorvo of the University of Pisa The conference is without registration fee, but registration is mandatory. There is a limited amount of support for PhD students who want to attend the event, application can be done through the registration form. Full information are available at the web-page: https://events.dm.unipi.it/event/280/ The organizing committee, P. Boito, G.M. Del Corso, F. Durastante, S. Gazzola, L. Heltai, S. Massei, C. Pagliantini, F. Poloni, L. Robol.

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[Indico] Taejun Park, A low-rank approximation of parameter-dependent matrices via CUR decomposition, 13/06/2024, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 31 May '24

31 May '24

Title: A low-rank approximation of parameter-dependent matrices via CUR decomposition, Speaker(s): Taejun Park, University of Oxford, Date and time: 13 Jun 2024, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/285 Abstract -------- Finding a low-rank approximation for parameter-dependent matrices $A(t)$ is an important task appearing in dynamical systems and image series compression. In this talk, we present an efficient randomized algorithm that computes a low-rank approximation of $A(t)$ at finite specified parameter values using the CUR decomposition. The key idea lies in reusing the same or a similar set of column and row indices for the CUR decomposition at nearby parameter values. The resulting algorithm is rank-adaptive, certifiable and has complexity that compares favorably to existing methods. This is joint work with Yuji Nakatsukasa. -- Indico :: Email Notifier https://events.dm.unipi.it/e/285

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Reminder: seminar of the quantum series. Taday at 15:00 G. De Palma
by Gianna M. Del Corso 27 May '24

27 May '24

This is a reminder for today’s seminar: Title: Quantum neural networks are Gaussian processes Speaker: Giacomo De Palma (University of Bologna) Venue: sala Galilei, room 131, Ed. C, Polo Fibonacci Time: Monday, 27/05/2024, 15:00 Here the link for attending online https://teams.microsoft.com/l/meetup-join/19%3ameeting_YWY5ZTRjN2MtOWI5OC00… <https://teams.microsoft.com/l/meetup-join/19:meeting_YWY5ZTRjN2MtOWI5OC00OD…> Gianna @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@

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[Indico] Dierk Schleicher, The Weierstrass and Ehrlich-Aberth root finders as dynamical systems, 24/05/2024, 16:00 Europe/Rome
by leonardo.robol＠unipi.it 23 May '24

23 May '24

Title: The Weierstrass and Ehrlich-Aberth root finders as dynamical systems, Speaker(s): Dierk Schleicher, Aix-Marseille Université, Date and time: 24 May 2024, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). You can access the full event here: https://events.dm.unipi.it/e/282 Abstract -------- Finding roots of complex polynomials in one variable is a fundamental challenge at the interface of theoretical and applied mathematics, as well as in many applications. Many methods have been proposed; the best known is Newton’s method that tries to find a single root at a time. There are several methods that try to approximate all roots at the same time. The best known are the Weierstrass—Durand—Kerner and Ehrlich—Aberth methods. These are known to work very well in practice, but little is known about their properties as global dynamical systems. We discuss various global dynamical properties, especially the search for attracting periodic orbits (which rule out general convergence) and orbits that diverge to infinity. This reports on joint work, partially still in progress, with Bernhard Reinke, Michael Stoll, and others. -- Indico :: Email Notifier https://events.dm.unipi.it/e/282

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[Indico] Dierk Schleicher, The Weierstrass and Ehrlich-Aberth root finders as dynamical systems, 24/05/2024, 16:00 Europe/Rome
by leonardo.robol＠unipi.it 20 May '24

20 May '24

Title: The Weierstrass and Ehrlich-Aberth root finders as dynamical systems, Speaker(s): Dierk Schleicher, Aix-Marseille Université, Date and time: 24 May 2024, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). You can access the full event here: https://events.dm.unipi.it/e/282 Abstract -------- Finding roots of complex polynomials in one variable is a fundamental challenge at the interface of theoretical and applied mathematics, as well as in many applications. Many methods have been proposed; the best known is Newton’s method that tries to find a single root at a time. There are several methods that try to approximate all roots at the same time. The best known are the Weierstrass—Durand—Kerner and Ehrlich—Aberth methods. These are known to work very well in practice, but little is known about their properties as global dynamical systems. We discuss various global dynamical properties, especially the search for attracting periodic orbits (which rule out general convergence) and orbits that diverge to infinity. This reports on joint work, partially still in progress, with Bernhard Reinke, Michael Stoll, and others. -- Indico :: Email Notifier https://events.dm.unipi.it/e/282

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Next week's seminar on quantum Computing : Monday 20 at 17:00 Oliver Morsch
by Gianna M. Del Corso 16 May '24

16 May '24

Dear All, As part of the CN1-SPOKE 10 on Quantum Computing, we are organizing a weekly seminar series. Next week's there will be: Title: Rydberg qubits for simulation and sensing Speaker: Oliver Morsch (CNR-INO and University of Pisa) Venue: Seminar room of Math department (1st floor on the left) Time: Monday, 20/05/2024, 17:00 Abstract: In recent years, Rydberg atoms have been increasingly used in several quantum technologies. In this talk I will give a brief introduction to Rydberg qubits and their applications in quantum simulation and quantum sensing. I will then give some examples of our recent work on these two technologies: the simulation of open quantum systems (phase transitions in driven quantum systems with controlled dissipation) and spatially resolved temperature measurements in a cold atomic gas using Rydberg- Doppler broadening thermometry. Everyone is welcome! GIanna @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@

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Next week's seminars on quantum Computing : Monday 6 and Friday 10
by Gianna M. Del Corso 02 May '24

02 May '24

Dear All, As part of the CN1-SPOKE 10 on Quantum Computing, we are organizing a weekly seminar series. This week, exceptionally we will have two seminars: Title: The effect of phase noise in superconducting qubit control Speaker: Agata Barsotti (Università di Pisa) Venue: room 250, first floor Ed. C, Polo Fibonacci (Physics Dept.) Time: Monday, 06/05/2024, 17:00 At the end of the same week there is: Title: Certified randomness from single-particle entanglement Speaker: Sonia Mazzucchi (Università di Trento) Venue: Sala Gerace, Ed. C Polo Fibonacci (Computer Science Dept.) Time: Friday, 10/05/2024, 16:00 The abstracts of both the seminars are attached. Everyone is welcome! Gianna Del Corso @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@

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Next week's seminar on quantum Computing : Today at 14:00 Lindsay Bassman Oftelie
by Gianna M. Del Corso 22 Apr '24

22 Apr '24

Dear all, this message is a reminder for today's quantum series seminar. Title: Dynamic Cooling of Qubits on Contemporary Quantum Computers Speaker: Lindsay Bassman Oftelie (NEST-CNR) Venue: Sala Polifunzionale, Ed. C, Polo Fibonacci (Dip. Informatica) Time: Monday, 22/04/2024, 14:00 Abstract: Quantum computers require qubits to be initialized in a pure (i.e., cold) state for successful computation. Dynamic cooling offers a route to effectively lower qubit temperatures beyond what is possible with direct, physical cooling techniques. It works by cooling a subset of qubits, at the expense of heating others, by applying certain logic gates to the entire system. While it was initially dismissed as impractical for the high-temperature NMR-based quantum computers available at the time of its inception, we show how dynamic cooling is substantially more effective and efficient on the low-temperature quantum computers available today. In this talk, we will examine how optimal dynamic cooling scales with total system size, in terms of the minimal achievable final temperature, the work cost, and the complexity of the associated quantum circuits. We will observe the effect of hardware noise on cooling and we will propose a sub-optimal dynamic cooling scheme with fixed (low) complexity to improve the feasibility of implementation on noisy quantum hardware. Here the link for the online attendance https://teams.microsoft.com/l/meetup-join/19%3ameeting_YzgwYmY4NDMtZWUwZi00… <https://teams.microsoft.com/l/meetup-join/19:meeting_YzgwYmY4NDMtZWUwZi00Mz…> See you there. Gianna Del Corso @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@

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Next week's seminar on quantum Computing : Lindasy Bassman Oftelie
by Gianna M. Del Corso 16 Apr '24

16 Apr '24

Dear all, As part of the CN1-SPOKE 10 on Quantum Computing, we are organizing a weekly seminar series. Next week’s seminar is: Title: Dynamic Cooling of Qubits on Contemporary Quantum Computers Speaker: Lindsay Bassman Oftelie (NEST-CNR) Venue: Sala Polifunzionale, Ed. C, Polo Fibonacci (Dip. Informatica) Time: Monday, 22/04/2024, 14:00 Abstract: Quantum computers require qubits to be initialized in a pure (i.e., cold) state for successful computation. Dynamic cooling offers a route to effectively lower qubit temperatures beyond what is possible with direct, physical cooling techniques. It works by cooling a subset of qubits, at the expense of heating others, by applying certain logic gates to the entire system. While it was initially dismissed as impractical for the high-temperature NMR-based quantum computers available at the time of its inception, we show how dynamic cooling is substantially more effective and efficient on the low-temperature quantum computers available today. In this talk, we will examine how optimal dynamic cooling scales with total system size, in terms of the minimal achievable final temperature, the work cost, and the complexity of the associated quantum circuits. We will observe the effect of hardware noise on cooling and we will propose a sub-optimal dynamic cooling scheme with fixed (low) complexity to improve the feasibility of implementation on noisy quantum hardware. Everyone is welcome! Please, note the change of venue and time. ======================================================================= @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@

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[Indico] Ivan Bioli, Preconditioned Low-Rank Riemannian Optimization for Multiterm Linear Matrix Equations, 11/04/2024, 16:00 Europe/Rome
by fabio.durastante＠unipi.it 10 Apr '24

10 Apr '24

Title: Preconditioned Low-Rank Riemannian Optimization for Multiterm Linear Matrix Equations, Speaker(s): Ivan Bioli, Università degli Studi di Pavia, Date and time: 11 Apr 2024, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). You can access the full event here: https://events.dm.unipi.it/e/268 Abstract -------- We focus on the development and analysis of Riemannian optimization methods for solving multiterm linear matrix equations, when the associated linear operator is symmetric positive definite. Assuming low-rank approximability of the solution, we employ first- and second-order Riemannian optimization algorithms on low-rank matrix manifolds. To enhance competitiveness with existing solvers on realistic problems, significant efforts are dedicated to developing efficient Riemannian preconditioners, which are interpreted as changing the Riemannian metric. By alternating between fixed-rank Riemannian optimization and rank updates, we devise a rank-adaptive algorithm that does not require fixing the rank a priori. In numerical experiments, we illustrate the effectiveness of the developed Riemannian preconditioners, comparing our approach with established solvers such as Conjugate Gradient with truncation. Results indicate that the Riemannian optimization approach, in both its fixed-rank and rank-adaptive variants, is competitive with other solvers and can avoid excessive growth of ranks in intermediate iterations. References [Bou23] Nicolas Boumal. An Introduction to Optimization on Smooth Manifolds. 1st ed. Cambridge University Press, Mar. 16, 2023. [KSV16] Daniel Kressner, Michael Steinlechner, and Bart Vandereycken. “Preconditioned Low-rank Riemannian Optimization for Linear Systems with Tensor Product Structure”. In: SIAM Journal on Scientific Computing 38.4 (Jan. 2016), A2018–A2044. [VV10] Bart Vandereycken and Stefan Vandewalle. “A Riemannian Optimization Ap proach for Computing Low-Rank Solutions of Lyapunov Equations”. In: SIAM Journal on Matrix Analysis and Applications 31.5 (Jan. 2010), pp. 2553–2579. -- Indico :: Email Notifier https://events.dm.unipi.it/e/268

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Next week's seminar on quantum Computing : Leonardo Banchi
by Gianna M. Del Corso 05 Apr '24

05 Apr '24

Dear all, As part of the CN1-SPOKE 10 on Quantum Computing, we are organizing a weekly seminar series. Next week’s seminar is: Title: Statistical Complexity of Quantum Learning Speaker: Leonardo Banchi (Università degli Studi di Firenze) Venue: Room 250, Ed. C, Polo Fibonacci (Physics Department, first floor) Time: Monday, 08/04/2024, 17:00 Abstract: Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning problems involve settings in which the mechanism generating the data is unknown, and the main goal of a learning algorithm is to ensure satisfactory accuracy levels when only given access to data and, possibly, side information such as expert knowledge. I will introduce the complexity of quantum learning using information-theoretic techniques by focusing on data complexity, copy complexity, and model complexity. Copy complexity arises from the destructive nature of quantum measurements, which irreversibly alter the state to be processed, limiting the information that can be extracted about quantum data. For example, in a quantum system, unlike in classical machine learning, it is generally not possible to evaluate the training loss simultaneously on multiple hypotheses using the same quantum data. To make the seminar approachable by different research communities, I will provide extensive background material on classical results from statistical learning theory, as well as on the distinguishability of quantum states. Throughout, we highlight the differences between quantum and classical learning by addressing both supervised and unsupervised learning, and discuss potential advantages. Reference: arXiv:2309.11617 - Adv. Quant. Tech 2024 - in press Everyone is welcome! @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@

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[Indico] Ivan Bioli, Preconditioned Low-Rank Riemannian Optimization for Multiterm Linear Matrix Equations, 11/04/2024, 16:00 Europe/Rome
by fabio.durastante＠unipi.it 03 Apr '24

03 Apr '24

Title: Preconditioned Low-Rank Riemannian Optimization for Multiterm Linear Matrix Equations, Speaker(s): Ivan Bioli, École Polytechnique Fédérale de Lausanne, Date and time: 11 Apr 2024, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). You can access the full event here: https://events.dm.unipi.it/e/268 Abstract -------- We focus on the development and analysis of Riemannian optimization methods for solving multiterm linear matrix equations, when the associated linear operator is symmetric positive definite. Assuming low-rank approximability of the solution, we employ first- and second-order Riemannian optimization algorithms on low-rank matrix manifolds. To enhance competitiveness with existing solvers on realistic problems, significant efforts are dedicated to developing efficient Riemannian preconditioners, which are interpreted as changing the Riemannian metric. By alternating between fixed-rank Riemannian optimization and rank updates, we devise a rank-adaptive algorithm that does not require fixing the rank a priori. In numerical experiments, we illustrate the effectiveness of the developed Riemannian preconditioners, comparing our approach with established solvers such as Conjugate Gradient with truncation. Results indicate that the Riemannian optimization approach, in both its fixed-rank and rank-adaptive variants, is competitive with other solvers and can avoid excessive growth of ranks in intermediate iterations. References [Bou23] Nicolas Boumal. An Introduction to Optimization on Smooth Manifolds. 1st ed. Cambridge University Press, Mar. 16, 2023. [KSV16] Daniel Kressner, Michael Steinlechner, and Bart Vandereycken. “Preconditioned Low-rank Riemannian Optimization for Linear Systems with Tensor Product Structure”. In: SIAM Journal on Scientific Computing 38.4 (Jan. 2016), A2018–A2044. [VV10] Bart Vandereycken and Stefan Vandewalle. “A Riemannian Optimization Ap proach for Computing Low-Rank Solutions of Lyapunov Equations”. In: SIAM Journal on Matrix Analysis and Applications 31.5 (Jan. 2010), pp. 2553–2579. -- Indico :: Email Notifier https://events.dm.unipi.it/e/268

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Next seminar on Quantum Computing : Simone Montangero Monday 25 h.16:00
by Gianna M. Del Corso 21 Mar '24

21 Mar '24

Dear All, As part of the CN1-SPOKE 10 on Quantum Computing, we are organizing a weekly seminar series. Next week’s seminar is: Title: Platforms and methods for quantum computing Speaker: Simone Montangero (University of Padova) Venue: Sala Gerace, Dipartimento di Informatica Time: Monday, 25/03/2024, 16:00 Abstract: We present an overview of the current status of the quantum computing landscape, presenting some fo the most developed hardware platforms together with a selection of recent results and methods currently driving the technological development of this potentially disruptive technology. Everyone is welcome! PS. Note that the seminar is at 4:00PM and not at 5Pm as usual ============================================================================== @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@

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Seminario CN1-SPOKE 10 (Quantum Computing) today
by Gianna M. Del Corso 11 Mar '24

11 Mar '24

Dear All, As part of the CN1-SPOKE 10 on Quantum Computing, we are organizing a weekly seminar series. This week’s seminar is: Title: Hybrid Variational Algorithms for Classical and Quantum Complex Systems Speaker: Elisa Ercolessi (University of Bologna) Venue: Sala Galilei, room 131 ground floor, Bldg C (Dipartimento di Fisica) Time: Monday, 11/03/2024, 17:00 Abstract: Quantum Computing is seen as a potential breakthrough for the study of hard classical problems as well as for quantum many body systems. However, we are in the era of NISQ devices and still far away from fault-tolerant machines. This leads us to consider the possibility of hybrid classical-quantum protocols of variational type: they exploit quantum resources to efficiently prepare states that depend on a suitable chosen set of variational parameters, which can then be determined by means of optimization algorithms to be run on a classical computer. The choice of such classical optimizer schemes is to be guided by compatibility requirements with respect to current available quantum platforms. To evaluate the feasibility of such an approach, we present different applications of the Quantum Approximate Optimization Algorithm to both classical and quantum systems implemented by means of emulations of the full protocol on a classical hardware as well as a case study that has been run on a real Rydberg atom quantum machine. Everyone is welcome! Gianna @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@

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seminar by Puya Latafat on Tue 27
by Giancarlo Bigi 26 Feb '24

26 Feb '24

You are very welcome to attend the seminar below Best wishes Giancarlo ============ _/Time/_: Tuesday 27 February, 11:00 am _/Place/_: Sala Seminari Est, Dipartimento di Informatica /_Speaker_/: Puya Latafat, KU Leuven /_Title_: / Convergence of operator splitting methods for nonmonotone inclusions /_Abstract_/ Despite their popularity, convergence results of splitting methods have been largely limited to the convex/monotone setting. We present convergence results for several first-order methods, including the proximal point method, forward-backward-forward splitting, and Douglas-Rachford splitting, within a nonmonotone setting. To this end, we focus on a problem class characterized by an oblique weak Minty condition, which captures non-trivial structures as we demonstrate with examples. Moreover, we introduce the concept of semimonotonicity and provide sufficient conditions for the global convergence of splitting techniques for the sum of two semimonotone operators. Illustrative examples demonstrate the wide range of problems our theory is able to cover.

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26/02/2024 - Seminario CN1-SPOKE 10 (Quantum Computing)
by Paola Boito 23 Feb '24

23 Feb '24

Dear all, I am forwarding this seminar announcement on quantum computing, which may be of interest to some of you. Best regards, Paola Boito ============================================================================== Dear All, As part of the CN1-SPOKE 10 on Quantum Computing, we are organizing a* weekly* seminar series. This week’s seminar is: Title: *Quantum Software Engineering* Speakers: *Giuseppe Bisicchia and Antonio Brogi * Venue:* Sala Gerace, Dipartimento di Informatica* Time:* Monday, 26/02/2024, 17:00 * Everyone is welcome! ==============================================================================

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[Indico] Dr Stefano Pozza, How to express the solution of an ODE as a linear system (in a suitable algebra) and exploit it for fast computation., 13/02/2024, 15:00 Europe/Rome
by fabio.durastante＠unipi.it 12 Feb '24

12 Feb '24

Title: How to express the solution of an ODE as a linear system (in a suitable algebra) and exploit it for fast computation., Speaker(s): Dr Stefano Pozza, Charles University, Date and time: 13 Feb 2024, 15:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Scuola Normale Superiore (Aula Mancini). Address: P.za dei Cavalieri, 7, 56126 Pisa PI You can access the full event here: https://events.dm.unipi.it/e/254 -- Indico :: Email Notifier https://events.dm.unipi.it/e/254

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[Indico] Prof. Dario Fasino, Is there a Kemeny’s constant for second-order random walks?, 06/02/2024, 10:00 Europe/Rome
by fabio.durastante＠unipi.it 05 Feb '24

05 Feb '24

Title: Is there a Kemeny’s constant for second-order random walks?, Speaker(s): Prof. Dario Fasino, Università di Udine, Date and time: 6 Feb 2024, 10:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). Address: Largo Bruno Pontecorvo, 5 – 56127 Pisa You can access the full event here: https://events.dm.unipi.it/e/258 Abstract -------- Kemeny's constant is a measure of the navigability of a network by ordinary random walks, which appears in a famous result on Markov chains known as the Random Target Lemma. A second-order random walk is a random walk where the transition probabilities depend on two past states. It can be turned into a Markov chain by lifting the state space from the nodes to the directed edges of the graph. The corresponding Kemeny constant is well known but says very little about the second-order walk on the original network. We extend certain definitions and results on standard random walk's mean hitting and return times to the second-order case and provide simple formulas that allow us to compute these numbers by solving suitable systems of linear equations. New results show that there is an infinite family of graphs for which certain second-order random walks, including the best-known non-backtracking random walk, satisfy a precise second-order counterpart of the Random Target Lemma. So, in summary, the answer to the question in the title is: Yes, sometimes. -- Indico :: Email Notifier https://events.dm.unipi.it/e/258

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[Indico] Prof. Dario Fasino, Is there a Kemeny’s constant for second-order random walks?, 2/6/24, 10:00 AM Europe/Rome
by fabio.durastante＠unipi.it 02 Feb '24

02 Feb '24

Title: Is there a Kemeny’s constant for second-order random walks?, Speaker(s): Prof. Dario Fasino, Università di Udine, Date and time: Feb 6, 2024, 10:00 AM (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). Address: Largo Bruno Pontecorvo, 5 – 56127 Pisa You can access the full event here: https://events.dm.unipi.it/e/258 Abstract -------- Kemeny's constant is a measure of the navigability of a network by ordinary random walks, which appears in a famous result on Markov chains known as the Random Target Lemma. A second-order random walk is a random walk where the transition probabilities depend on two past states. It can be turned into a Markov chain by lifting the state space from the nodes to the directed edges of the graph. The corresponding Kemeny constant is well known but says very little about the second-order walk on the original network. We extend certain definitions and results on standard random walk's mean hitting and return times to the second-order case and provide simple formulas that allow us to compute these numbers by solving suitable systems of linear equations. New results show that there is an infinite family of graphs for which certain second-order random walks, including the best-known non-backtracking random walk, satisfy a precise second-order counterpart of the Random Target Lemma. So, in summary, the answer to the question in the title is: Yes, sometimes. -- Indico :: Email Notifier https://events.dm.unipi.it/e/258

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[Indico] Dr Stefano Pozza, How to express the solution of an ODE as a linear system (in a suitable algebra) and exploit it for fast computation., 2/13/24, 3:00 PM Europe/Rome
by fabio.durastante＠unipi.it 25 Jan '24

25 Jan '24

Title: How to express the solution of an ODE as a linear system (in a suitable algebra) and exploit it for fast computation., Speaker(s): Dr Stefano Pozza, Charles University, Date and time: Feb 13, 2024, 3:00 PM (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Scuola Normale Superiore (Aula Mancini). Address: P.za dei Cavalieri, 7, 56126 Pisa PI You can access the full event here: https://events.dm.unipi.it/e/254 Abstract -------- The solution of systems of non-autonomous linear ordinary differential equations is crucial in various applications, such as nuclear magnetic resonance spectroscopy. We introduced a new solution expression in terms of a generalization of the Volterra composition. Such an expression is linear in a particular algebraic structure of distributions, which can be mapped onto a subalgebra of infinite matrices. It is possible to exploit the new expression to devise fast numerical methods for linear non-autonomous ODEs. As a first example, we present a new method for the operator solution of the generalized Rosen-Zener model, a system of linear non-autonomous ODEs from quantum mechanics. The new method’s computing time scales linearly with the model’s size in the numerical experiments. -- Indico :: Email Notifier https://events.dm.unipi.it/e/254

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Posizione tenure-track (RTT) al dipartimento di informatica
by Federico Poloni 24 Jan '24

24 Jan '24

Buongiorno, segnalo che è uscito il bando per una posizione RTT in analisi numerica (MAT/08) al dipartimento di informatica. Bando e istruzioni per fare domanda sono disponibili su https://bandi.unipi.it/public/Bandi/Detail/b34b7404-9d5a-4180-81e2-bd461bfe… . La scadenza per le domande è il 23 febbraio alle 13:00. La posizione è riservata a coloro che hanno trascorso un periodo di almeno 36 mesi in incarichi di ricerca o corsi di dottorato /al di fuori/ dell'università di Pisa. Tutti gli interessati sono invitati a partecipare! -- --Federico Poloni Dipartimento di Informatica, Università di Pisa https://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Fwd: I: 'TENORS' Marie Sklodowska Curie Network -- PhD positions available
by Paola Boito 27 Dec '23

27 Dec '23

Dear all, I would like to share this message from Iacopo Carusotto (iacopo.carusotto(a)unitn.it) in case someone you know is interested in the PhD positions advertised below. Best wishes, Paola Boito --------------------------------------------------- TENORS (*T*ensor mod*E*li*N*g, ge*O*met*R*y and optimi*S*ation) is a Marie Skłodowska-Curie Doctoral Network / Joint Doctorate (2024-2027), offering * * * 15 PhD positions.* The objective of TENORS is to conduct advanced research that addresses critical challenges in the fields of *tensor modeling and computation*, joining forces from *algebraic geometry, global optimisation, numerical computation, high performance computing, data science, quantum physics.* It aims to feed an innovative and ambitious *joint-PhD program* to train highly qualified young scientists in new scientific and technological knowledge. The PhD candidates will obtain joint/double PhD diplomas from reputed universities within TENORS project. For more information on TENORS see http://tenors-network.eu/ <http://tenors-network.eu/> Application deadline: March 31st, 2024. How to apply: https://project.inria.fr/tenors/phd-positions/ <https://project.inria.fr/tenors/phd-positions/> Where to submit your application: https://easychair.org/my/conference?conf=tenors2427 <https://easychair.org/my/conference?conf=tenors2427>

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Seminario PYSANUM Alessandro Filippo
by Nikita DENISKIN 11 Dec '23

11 Dec '23

Carǝ tuttǝ, Vi segnalo che domani *12 dicembre* alle ore *16:00* ci sarà un seminario tenuto da Alessandro Filippo (Roma Tor Vergata) in *Aula Seminari*. I seminari PYSANUM sono dei seminari informali di analisi numerica e matematica applicata rivolti a studenti, organizzati da alcuni dottorandi Unipi e SNS, con l'obiettivo di presentare in maniera accessibile argomenti di ricerca di analisi numerica ad un pubblico studentesco. Si possono trovare ulteriori informazioni sul nostro sito <https://pysanum.dm.unipi.it/>. A presto, Nikita ----- Titolo: *"Reti complesse: Robustezza, indici di centralità e nuove strategie per il ranking dei nodi"* Abstract: Determinare quali siano i nodi più importanti in una rete complessa è uno dei problemi principali dell’analisi delle reti. Tale problema, anche noto come il problema del ranking, viene tipicamente risolto attraverso il calcolo delle misure di centralità. Tuttavia, cambiamenti strutturali improvvisi, quali la rimozione di alcuni nodi o archi, possono invalidare la nostra conoscenza dei nodi più critici. Per esempio, nodi dapprima cruciali potrebbero perdere tutta la loro importanza qualora rimanessero isolati. Quindi, per studiare l’impatto della rimozione dei nodi più influenti da una rete, sarebbe necessario ricalcolare costantemente le misure di centralità, un’operazione spesso impraticabile per reti di grandi dimensioni. Al contrario, evitare del tutto il ricalcolo potrebbe fornire una rappresentazione della realtà poco accurata. In questo talk illustrerò due nuove strategie per ridurre il costo computazionale del calcolo sequenziale delle centralità, fornendo giustificazioni teoriche a supporto. Infine, mostrerò come sia possibile impiegare queste strategie per valutare la robustezza di una rete ad attacchi mirati. Tratto da un lavoro in collaborazione con Daniele Bertaccini. D. Bertaccini, A. Filippo. *A proposal for ranking through selective computation of centrality measures*. PLOS ONE, 18, 2023.

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Seminario PYSANUM Martina Iannacito
by Igor SIMUNEC 24 Nov '23

24 Nov '23

Carǝ tuttǝ, Vi scrivo per segnalare che lunedì 27 novembre Martina Iannacito (KU Leuven) terrà un seminario in Aula Riunioni alle 16.00, nell'ambito del ciclo di seminari PYSANUM. Di seguito titolo e abstract della presentazione. I seminari PYSANUM sono dei seminari informali di analisi numerica e matematica applicata rivolti a studenti, organizzati da alcuni dottorandi Unipi e SNS, con l'obiettivo di presentare in maniera accessibile argomenti di ricerca di analisi numerica ad un pubblico studentesco. Si possono trovare ulteriori informazioni sul nostro sito <https://pysanum.dm.unipi.it/>. A presto, Igor ----- Titolo: Introduzione ai tensori: dalle applicazioni alle sfide contemporanee Abstract: Per oltre un secolo, i matematici sono stati affascinati dallo studio delle proprietà di famiglie di matrici. Gli oggetti con cui allora iniziarono a confrontarsi sono oggi noti come tensori o array multidirezionali. Lo studio dei tensori ha acquisito particolare rilevanza grazie alle molteplici applicazioni in cui forniscono importanti benefici. Queste strutture matematiche multidimensionali garantiscono l’unicità della fattorizzazione (sotto ipotesi non eccessivamente complesse), consentono rappresentazioni più adatte di fenomeni complessi e delle loro intricate interazioni. Infine, se rappresentati in modo ottimale, i tensori offrono vantaggi computazionali. Tutte queste loro proprietà hanno aperto diverse nuove direzioni di ricerca in campo matematico, numerico e computazionale. Nella prima metà di questa presentazione, esamineremo problemi provenienti da applicazioni concrete in cui i tensori sono stati di innovazione. Contemporaneamente, verrà fornita una panoramica di alcune tecniche di decomposizione tensoriale che meglio si adattano al problema considerato di volta in volta. Il focus della seconda parte si sposterà sulle sfide contemporanee incontrate nello sviluppo di tecniche basate su array multidimensionali, e nell’implementazione di nuovi algoritmi per la fattorizzazione tensoriale. Questa discussione offrirà spunti di riflessione sul panorama in evoluzione della ricerca sui tensori, evidenziandone la rilevanza e il potenziale.

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Nuova edizione del reading course: Riemannian Optimization (17/11, 16:00, Aula Riunioni)
by Fabio Durastante 25 Oct '23

25 Oct '23

Buonasera, A seguito del voto, l'argomento scelto per questa nuova edizione del Reading Course sarà /Riemannian Optimization/; abbiamo impostato una bozza di programma e contattato alcuni di voi per iniziare (in modo da concedere il tempo per preparare il materiale): il primo incontro sarà il 17/11 alle 16:00, in Aula Riunioni. Trovate tutti i dettagli qui: https://numpi.dm.unipi.it/reading-course-in-numerical-analysis/ C'è ancora spazio per candidarsi a tenere gli altri incontri. A presto! Fabio, Leonardo e Stefano.

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Reading Course Analisi Numerica 2024
by Fabio Durastante 11 Oct '23

11 Oct '23

Carə tuttə, Vi scriviamo perché abbiamo l'intenzione di ripartire con una nuova edizione del Reading Course Analisi Numerica. Si tratta di una serie di incontri dove verranno presentati alcuni risultati recenti vicini ad argomenti di ricerca di interesse, solitamente da studentə e/o dottorandə. Ogni iterazione del corso è dedicata ad un argomento specifico, e può essere seguito in modo indipendente dagli altri. Le proposta per questo semestre è una tra: - Ottimizzazione Riemanniana, - Operatori di Koopman. Aiutateci a decidere tra le due compilando il seguente form (su cui trovate anche alcune informazioni bibliografiche e contenutistiche sulle due proposte): - https://forms.gle/QfHpfE1WdjJH9Z6Q8 Se avete idee riguardo altri possibili argomenti che volete suggerire potete inserirle all'interno del modulo, insieme a delle preferenze orientative per il giorno di svolgimento. Trovate ulteriori informazioni sulle passate edizioni sul sito: - https://numpi.dm.unipi.it/reading-course-in-numerical-analysis/ E potete restare aggiornati sugli sviluppi iscrivendovi alla mailing list: - https://lists.dm.unipi.it/postorius/lists/reading-num.lists.dm.unipi.it/ A parte queste mail di annuncio, le informazioni riguardanti l'organizzazione circoleranno /unicamente/ sulla mailing list dedicata, per cui se siete interessati a seguire il corso iscrivetevi lì. Avete tempo per esprime le vostre preferenze fino a *Mercoledì 18 Ottobre* (incluso). Cordiali saluti, Fabio Durastante, Stefano Massei & Leonardo Robol

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[Indico] Mrs Lu Xia, On the influence of stochastic rounding bias in implementing gradient descent with applications in low-precision training, 18/07/2023, 14:00 Europe/Rome
by stefano.massei＠unipi.it 16 Jul '23

16 Jul '23

Title: On the influence of stochastic rounding bias in implementing gradient descent with applications in low-precision training, Speaker(s): Mrs Lu Xia, Eindhoven University of Technology, Date and time: 18 Jul 2023, 14:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/201 Abstract -------- In the context of low-precision computation for the training of neural networks with thegradient descent method (GD), the occurrence of deterministic rounding errors often leadsto stagnation or adversely affects the convergence of the optimizers. The employ-ment of unbiased stochastic rounding (SR) may partially capture gradient updates thatare lower than the minimum rounding precision, with a certain probability. Weprovide a theoretical elucidation for the stagnation observed in GD when training neuralnetworks with low-precision computation. We analyze the impact of floating-point round-off errors on the convergence behavior of GD with a particular focus on convex problems.Two biased stochastic rounding methods, signed-SR$_\varepsilon$ and SR$_\varepsilon$, are proposed, which havebeen demonstrated to eliminate the stagnation of GD and to result in significantly fasterconvergence than SR in low-precision floating-point computation.We validate our theoretical analysis by training a binary logistic regression model onthe Cifar10 database and a 4-layer fully-connected neural network model on the MNISTdatabase, utilizing a 16-bit floating-point representation and various rounding techniques.The experiments demonstrate that signed-SR$_\varepsilon$ and SR$_\varepsilon$ may achieve higher classificationaccuracy than rounding to the nearest (RN) and SR, with the same number of trainingepochs. It is shown that a faster convergence may be obtained by the new roundingmethods with 16-bit floating-point representation than by RN with 32-bit floating-pointrepresentation. -- Indico :: Email Notifier https://events.dm.unipi.it/e/201

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[Indico] Mrs Lu Xia, On the influence of stochastic rounding bias in implementing gradient descent with applications in low-precision training, 18/07/2023, 14:00 Europe/Rome
by stefano.massei＠unipi.it 10 Jul '23

10 Jul '23

Title: On the influence of stochastic rounding bias in implementing gradient descent with applications in low-precision training, Speaker(s): Mrs Lu Xia, Eindhoven University of Technology, Date and time: 18 Jul 2023, 14:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/201 Abstract -------- In the context of low-precision computation for the training of neural networks with thegradient descent method (GD), the occurrence of deterministic rounding errors often leadsto stagnation or adversely affects the convergence of the optimizers. The employ-ment of unbiased stochastic rounding (SR) may partially capture gradient updates thatare lower than the minimum rounding precision, with a certain probability. Weprovide a theoretical elucidation for the stagnation observed in GD when training neuralnetworks with low-precision computation. We analyze the impact of floating-point round-off errors on the convergence behavior of GD with a particular focus on convex problems.Two biased stochastic rounding methods, signed-SR$_\varepsilon$ and SR$_\varepsilon$, are proposed, which havebeen demonstrated to eliminate the stagnation of GD and to result in significantly fasterconvergence than SR in low-precision floating-point computation.We validate our theoretical analysis by training a binary logistic regression model onthe Cifar10 database and a 4-layer fully-connected neural network model on the MNISTdatabase, utilizing a 16-bit floating-point representation and various rounding techniques.The experiments demonstrate that signed-SR$_\varepsilon$ and SR$_\varepsilon$ may achieve higher classificationaccuracy than rounding to the nearest (RN) and SR, with the same number of trainingepochs. It is shown that a faster convergence may be obtained by the new roundingmethods with 16-bit floating-point representation than by RN with 32-bit floating-pointrepresentation. -- Indico :: Email Notifier https://events.dm.unipi.it/e/201

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Fwd: [Random] (PMS)^2 talk - Cazzaniga - July 3 at 17.00
by Federico Poloni 27 Jun '23

27 Jun '23

Inoltro anche su questa lista, visto che l'argomento può essere interessante. Un saluto a tutti! Federico -------- Forwarded Message -------- Subject: [Random] (PMS)^2 talk - Cazzaniga - July 3 at 17.00 Date: Tue, 27 Jun 2023 15:48:24 +0200 From: Carlo Orrieri <carlo.orrieri(a)unipv.it> To: random(a)fields.dm.unipi.it Dear colleagues, We are happy to announce the following *hybrid - that is, in person with online streaming -* talk: Speaker: *Alberto Cazzaniga*** (Area Science Park) Title: What is the probability that a random symmetric tensor is close to rank-one? *Abstract*: We address the problem of estimating the probability that a real symmetric tensor is close to rank-one tensors, motivated by the many applications of low-rank approximation. We discuss how the question can be addressed by studying metric invariants of the real Veronese variety thanks to the Weyl's tube formula. We describe the role of the reach and the curvature coefficients with respect to the Bombieri-Weyl metric in obtaining an explicit estimate, and outline the main ideas employed to tackle their calculation. We conclude by discussing some asymptotic results for the case of rational normal curves. Based on joint work with A. Lerario and A. Rosana. Date and time: *Monday July 3, 17:00-18:00 (Rome time zone)* Place: Laboratorio didattico*, dipartimento di matematica dell’università di Pavia, via Ferrata 5, Pavia.* Entra nella riunione in Zoom https://us02web.zoom.us/j/81154155086?pwd=Rit2Ymd3eE1lUWIrc0ErQlRMcGNVdz09 <https://us02web.zoom.us/j/81154155086?pwd=Rit2Ymd3eE1lUWIrc0ErQlRMcGNVdz09> ID riunione: 811 5415 5086 Passcode: 317594 This talk is part of the *(PMS)^2: Pavia-Milano Seminar series on Probability and Mathematical Statistics* organized jointly by the universities Milano-Bicocca, Pavia, Milano-Politecnico. Participation is free and welcome! Best regards The organizers (Carlo Orrieri, Maurizia Rossi, Margherita Zanella)

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[Indico] Luca Saluzzi, A Tensor Gradient Cross for Hamilton-Jacobi-Bellman equations, 05/06/2023, 16:00 Europe/Rome
by leonardo.robol＠unipi.it 05 Jun '23

05 Jun '23

Title: A Tensor Gradient Cross for Hamilton-Jacobi-Bellman equations, Speaker(s): Luca Saluzzi, Scuola Normale Superiore, Pisa, Date and time: 5 Jun 2023, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). You can access the full event here: https://events.dm.unipi.it/e/199 Abstract -------- Hamilton-Jacobi-Bellman (HJB) equation plays a central role in optimal control and differential games, enabling the computation of robust controls in feedback form. The main disadvantage for this approach depends on the so-called curse of dimensionality, since the HJB equation and the dynamical system live in the same, possibly high dimensional, space. In this talk, I will present a data-driven method for approximating high-dimensional HJB equations based on tensor decompositions. The approach presented in this talk is based on the knowledge of the value function and its gradient on sample points and on a tensor train decomposition of the value function. The collection of the data will be derived by two possible techniques: Pontryagin Maximum Principle and State-Dependent Riccati Equations. The numerical experiments will demonstrate an at most linear complexity in the dimension and a better stability in presence of noise. Moreover, I will present an application to an agent-based model and a comparison with Deep Learning techniques. Finally, time permitting, I will consider the coupling of the proposed method with Model Order Reduction techniques and their application to boundary feedback control for the Navier-Stokes equations. -- Indico :: Email Notifier https://events.dm.unipi.it/e/199

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[Indico] Michele Rinelli, Stochastic probing methods for estimating the trace of functions of sparse symmetric matrices, 30/05/2023, 16:00 Europe/Rome
by fabio.durastante＠unipi.it 29 May '23

29 May '23

Title: Stochastic probing methods for estimating the trace of functions of sparse symmetric matrices, Speaker(s): Michele Rinelli, Scuola Normale Superiore, Date and time: 30 May 2023, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/198 Abstract -------- We consider the combination of two approaches for the trace estimation of a symmetric matrix function f(A) when the only feasible operations are matrix-vector products and quadratic forms with f(A): stochastic estimators, such as the Hutchinson estimator and its refined variants Hutch++ and the recent XTrace, and probing methods based on graph colorings. Particularly effective is the case where we replace the indicator vectors for the coloring used in probing by random vectors whose non-zero entries have Rademacher distribution. A theoretical analysis exposes conditions under which using just one Rademacher probing vector per color is provably better than the classical probing approach. Numerical experiments show that existing methods are also outperformed under suitable conditions on the sparsity pattern of A and on the spectrum of f(A). This talk is based on a joint work with Andreas Frommer and Marcel Schweitzer. -- Indico :: Email Notifier https://events.dm.unipi.it/e/198

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[Indico] Michele Rinelli, Stochastic probing methods for estimating the trace of functions of sparse symmetric matrices, 30/05/2023, 16:00 Europe/Rome
by fabio.durastante＠unipi.it 23 May '23

23 May '23

Title: Stochastic probing methods for estimating the trace of functions of sparse symmetric matrices, Speaker(s): Michele Rinelli, Scuola Normale Superiore, Date and time: 30 May 2023, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/198 Abstract -------- We consider the combination of two approaches for the trace estimation of a symmetric matrix function f(A) when the only feasible operations are matrix-vector products and quadratic forms with f(A): stochastic estimators, such as the Hutchinson estimator and its refined variants Hutch++ and the recent XTrace, and probing methods based on graph colorings. Particularly effective is the case where we replace the indicator vectors for the coloring used in probing by random vectors whose non-zero entries have Rademacher distribution. A theoretical analysis exposes conditions under which using just one Rademacher probing vector per color is provably better than the classical probing approach. Numerical experiments show that existing methods are also outperformed under suitable conditions on the sparsity pattern of A and on the spectrum of f(A). This talk is based on a joint work with Andreas Frommer and Marcel Schweitzer. -- Indico :: Email Notifier https://events.dm.unipi.it/e/198

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Fwd: POSTDOC at AROMATH, Inria of Université Côte d'Azur.
by Paola Boito 23 May '23

23 May '23

Dear all, I am forwarding this announcement in case anyone is interested. All the best, Paola -------- Forwarded Message -------- Subject: [DKIM Failed - Firma mittente non verificata][gdrmoa] POSTDOC at AROMATH, Inria of Université Côte d'Azur. Date: Tue, 23 May 2023 10:16:57 +0200 From: Bernard Mourrain <Bernard.Mourrain(a)inria.fr> Reply-To: Bernard Mourrain <Bernard.Mourrain(a)inria.fr> To: gdrmoa(a)listes.math.cnrs.fr Dear Colleagues, A POSTDOC position is available in Aromath <https://es.sonicurlprotection-fra.com/click?PV=2&MSGID=20230523083043027614…> team at Inria of Université Côte d'Azur <https://es.sonicurlprotection-fra.com/click?PV=2&MSGID=20230523083043027614…>. The duration of the contract is _1+1 years (one year renewable one additional year)_. The starting date is flexible, ideally in fall 2023. Here is the link to the official announcement and to apply <https://es.sonicurlprotection-fra.com/click?PV=2&MSGID=20230523083043027614…> to the position. Please feel free to contact me for any questions you may have. Please also forward this message to any potential interested candidates you may know. Best regards, Bernard Mourrain

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Seminario Luca Heltai 26/5
by Beatrice Meini 22 May '23

22 May '23

Carissimi, vi inoltro il seguente annuncio di seminario, nell'ambito delle manifestazioni d'interesse del Progetto di Eccellenza. Saluti, Beatrice -------- Forwarded Message -------- Subject: [Personale.docente.dm] Prossimi seminari Dipartimento di Eccellenza Date: Mon, 22 May 2023 07:54:42 +0000 From: Maria Stella Gelli <maria.stella.gelli(a)unipi.it> To: personale.docente(a)dm.unipi.it <personale.docente(a)dm.unipi.it> Cari tutti, vi segnalo che venerdì alle ore 11.00 in Aula Magna si terrà il quarto dei seminari collegati alla manifestazione di interesse del Progetto di Eccellenza. Lo speaker è Luca Heltai (Sissa) https://www.dm.unipi.it/eventi/an-overview-on-non-matching-approximation-me… <https://www.dm.unipi.it/eventi/an-overview-on-non-matching-approximation-me…> I seminari proseguiranno nelle prossime settimane, potete seguire il calendario (in continua evoluzione) al seguente link https://www.dm.unipi.it/seminari-di-dipartimento/ <https://www.dm.unipi.it/seminari-di-dipartimento/> Vi segnaliamo sul canale Colloquia del Team Dipartimento di Matematica trovate la registrazione dei seminari passati, inoltre, a meno di problematiche dell'ultimo minuto, i seminari sono trasmessi in streaming sullo stesso canale. Cari saluti Maria Stella Gelli & Francesco Sala per il Direttore

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[Indico] Federica Pes, Grassmann extrapolation of density matrices as a tool to accelerate Born-Oppenheimer molecular dynamics, 19/05/2023, 15:00 Europe/Rome
by leonardo.robol＠unipi.it 16 May '23

16 May '23

Title: Grassmann extrapolation of density matrices as a tool to accelerate Born-Oppenheimer molecular dynamics, Speaker(s): Federica Pes, Università di Pisa, Date and time: 19 May 2023, 15:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/192 Abstract -------- Born-Oppenheimer molecular dynamics (BOMD) is a powerful but expensive technique. The main bottleneck in a density functional theory (DFT) BOMD calculation is the solution to the DFT nonlinear equations that requires an iterative procedure that starts from a guess for the density matrix. To speed up such calculations, various extrapolation strategies have been developed to use densities available at previous simulation steps as a guess for the iterative procedure. However, density matrices belong in a Grassmann manifold, which is not a vector space. Therefore the linear extrapolation is performed in a tangent space of the manifold, thanks to a locally bijective map between the manifold and its tangent space.In this contribution, we introduce an approximately time reversible approach to extrapolate density matrices. Some numerical experiments show optimal performance, compared to the state of the art. -- Indico :: Email Notifier https://events.dm.unipi.it/e/192

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Fwd: Faculty position Numerical Methods for Quantum Computing at KU Leuven
by Paola Boito 11 May '23

11 May '23

Buongiorno, inoltro questo annuncio per una posizione a KU Leuven. La posizione è nel gruppo di analisi numerica ed è orientata al quantum computing. A presto, Paola -------- Forwarded Message -------- Subject: Faculty position Numerical Methods for Quantum Computing at KU Leuven Date: Tue, 9 May 2023 13:15:26 +0200 From: Nick Vannieuwenhoven <nick.vannieuwenhoven(a)kuleuven.be> To: paola.boito(a)unipi.it Dear Prof. Paola Boito, We would like to draw your attention to the job offer for the full-time faculty position in /Numerical Methods for Quantum Computing/ at KU Leuven, with application deadline September 14, 2023. A short description is included below. A detailed description is available at https://www.kuleuven.be/personeel/jobsite/jobs/60205789 Since we believe that the position could be of interest to some of your group members, colleagues or collaborators, we would kindly ask you to forward the message, in particular to excellent post-docs and junior group leaders. Best regards, Nick Vannieuwenhoven ---- Prof. dr. Nick Vannieuwenhoven, Member of the search committee. KU Leuven, Department of Computer Science, Celestijnenlaan 200A, bus 2402, 3001 Heverlee, Belgium. *Faculty Position, Numerical Methods for Quantum Computing, KU Leuven * The Science, Engineering, and Technology Group of KU Leuven invites applications for a full time research professorship in the research unit Numerical Analysis and Applied Mathematics (NUMA). The research in NUMA covers many aspects of computational mathematics, including approximation theory, numerical integration, numerical (multi-) linear algebra, numerical partial differential equations, uncertainty quantification, optimization and control, discrete optimization and scheduling, and high-performance computing. The research unit also performs research in collaboration with industry. The new position aims to strengthen the experience in the domain of quantum computing. Quantum computing is a novel computing paradigm relying on fundamental properties of quantum physics. It features new core building blocks that can lead to exponential speedups relative to traditional computing. This requires a fundamental shift in the design of numerical algorithms and their optimized mapping to available quantum circuits. Candidates are expected to have already obtained excellent research results within the research field of design, analysis, development, and implementation of new quantum algorithms for numerical computing. The successful candidate is expected to develop a research program on quantum computing, ensure high-quality education within the area of mathematical engineering, and be prepared to provide scientific and administrative services. For further details, contact information and the application procedure (deadline September 14, 2023), follow the link: https://www.kuleuven.be/personeel/jobsite/jobs/60205789 The vacancy fits within the KU Leuven Quantum initiative: https://set.kuleuven.be/en/about-us/vacancies/quantum

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[Indico] Federica Pes, Grassmann extrapolation of density matrices as a tool to accelerate Born-Oppenheimer molecular dynamics, 19/05/2023, 15:00 Europe/Rome
by leonardo.robol＠unipi.it 06 May '23

06 May '23

Title: Grassmann extrapolation of density matrices as a tool to accelerate Born-Oppenheimer molecular dynamics, Speaker(s): Federica Pes, Università di Pisa, Date and time: 19 May 2023, 15:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/192 Abstract -------- Born-Oppenheimer molecular dynamics (BOMD) is a powerful but expensive technique. The main bottleneck in a density functional theory (DFT) BOMD calculation is the solution to the DFT nonlinear equations that requires an iterative procedure that starts from a guess for the density matrix. To speed up such calculations, various extrapolation strategies have been developed to use densities available at previous simulation steps as a guess for the iterative procedure. However, density matrices belong in a Grassmann manifold, which is not a vector space. Therefore the linear extrapolation is performed in a tangent space of the manifold, thanks to a locally bijective map between the manifold and its tangent space.In this contribution, we introduce an approximately time reversible approach to extrapolate density matrices. Some numerical experiments show optimal performance, compared to the state of the art. -- Indico :: Email Notifier https://events.dm.unipi.it/e/192

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[Indico] Prof. Vandebril Raf, Perfect Shifted QR for Rank Structured Pencils, 13/04/2023, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 11 Apr '23

11 Apr '23

Title: Perfect Shifted QR for Rank Structured Pencils, Speaker(s): Prof. Vandebril Raf, KU Leuven, Date and time: 13 Apr 2023, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/182 Abstract -------- It is known that executing a perfect shifted QR step via the implicit QR algorithm performs poor in terms of stability, and accuracy. Typically several steps are required before deflation actually takes place. This behavior can be remedied by determining the similarity transformation via the associated eigenvector. Similar techniques can be deduced for the QZ algorithm and the rational QZ algorithm. In this talk we generalize this even further and present an approach for executing a perfect shifted QR step for general rank structured pencils. We prove that the rank structures of the matrices involved in the pencil are preserved, and moreover we examine the preservation of spectral properties of subblocks in the pencil.Authors: Nicola Mastronardi, Marc Van Barel, Raf Vandebril, and Paul Van Dooren -- Indico :: Email Notifier https://events.dm.unipi.it/e/182

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[Indico] Cecilia Pagliantini, Model order reduction of parametric Hamiltonian systems on matrix manifolds, 28/03/2023, 16:00 Europe/Rome
by leonardo.robol＠unipi.it 27 Mar '23

27 Mar '23

Title: Model order reduction of parametric Hamiltonian systems on matrix manifolds, Speaker(s): Cecilia Pagliantini, University of Pisa, Date and time: 28 Mar 2023, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). You can access the full event here: https://events.dm.unipi.it/e/176 Abstract -------- Model order reduction of parametric differential equations aims at constructing low-complexity high-fidelity surrogate models that allow rapid and accurate solutions under parameter variation. The development of reduced order models for Hamiltonian systems is challenged by several factors: (i) failing to preserve the geometric structure encoding the physical properties of the dynamics, such as invariants of motion or symmetries, might lead to instabilities and unphysical behaviors of the resulting approximate solutions; (ii) the slowly decaying Kolmogorov n-width of transport-dominated and non-dissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations; and (iii) nonlinear operators require hyper-reduction techniques that preserve the gradient structure of the flow velocity.We will discuss how to address these aspects via a structure-preserving nonlinear reduced basis approach based on dynamical low-rank approximation. The gist of the proposed method is to adapt in time an approximate low-dimensional phase space endowed with the geometric structure of the full model and to ensure that the reduced flow is still Hamiltonian. -- Indico :: Email Notifier https://events.dm.unipi.it/e/176

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[Indico] Cecilia Pagliantini, Model order reduction of parametric Hamiltonian systems on matrix manifolds, 28/03/2023, 16:00 Europe/Rome
by leonardo.robol＠unipi.it 21 Mar '23

21 Mar '23

Title: Model order reduction of parametric Hamiltonian systems on matrix manifolds, Speaker(s): Cecilia Pagliantini, University of Pisa, Date and time: 28 Mar 2023, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). You can access the full event here: https://events.dm.unipi.it/e/176 Abstract -------- Model order reduction of parametric differential equations aims at constructing low-complexity high-fidelity surrogate models that allow rapid and accurate solutions under parameter variation. The development of reduced order models for Hamiltonian systems is challenged by several factors: (i) failing to preserve the geometric structure encoding the physical properties of the dynamics, such as invariants of motion or symmetries, might lead to instabilities and unphysical behaviors of the resulting approximate solutions; (ii) the slowly decaying Kolmogorov n-width of transport-dominated and non-dissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations; and (iii) nonlinear operators require hyper-reduction techniques that preserve the gradient structure of the flow velocity.We will discuss how to address these aspects via a structure-preserving nonlinear reduced basis approach based on dynamical low-rank approximation. The gist of the proposed method is to adapt in time an approximate low-dimensional phase space endowed with the geometric structure of the full model and to ensure that the reduced flow is still Hamiltonian. -- Indico :: Email Notifier https://events.dm.unipi.it/e/176

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[Indico] Prof. Lloyd N. Trefethen, Applications of AAA Rational Approximation, 21/02/2023, 11:00 Europe/Rome
by fabio.durastante＠unipi.it 20 Feb '23

20 Feb '23

Title: Applications of AAA Rational Approximation, Speaker(s): Prof. Lloyd N. Trefethen, Mathematical Institute, University of Oxford, Date and time: 21 Feb 2023, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Scuola Normale Superiore (Aula Volterra). Address: Piazza dei Cavalieri, 7 - 56126 Pisa You can access the full event here: https://events.dm.unipi.it/e/158 Abstract -------- Abstract:For the first time, a method has recently become available for fast computation of near-best rational approximations on arbitrary sets in the real line or complex plane: the AAA algorithm (Nakatsukasa-Sete-T. 2018). We will present the algorithm and then demonstrate a number of applications, includingdetection of singularities, model order reduction, analytic continuation, functions of matrices, nonlinear eigenvalue problems, interpolation of equispaced data, smooth extension of multivariate real functions, extrapolation of ODE and PDE solutions into the complex plane, solution of Laplace problems, conformal mapping, Wiener-Hopf factorization. Note ---- A reminder of tomorrow's seminar. -- Indico :: Email Notifier https://events.dm.unipi.it/e/158

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[Indico] Prof. Lloyd N. Trefethen, Applications of AAA Rational Approximation, 21/02/2023, 11:00 Europe/Rome
by fabio.durastante＠unipi.it 13 Feb '23

13 Feb '23

Title: Applications of AAA Rational Approximation, Speaker(s): Prof. Lloyd N. Trefethen, Mathematical Institute, University of Oxford, Date and time: 21 Feb 2023, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Scuola Normale Superiore (Aula Volterra). Address: Piazza dei Cavalieri, 7 - 56126 Pisa You can access the full event here: https://events.dm.unipi.it/e/158 Abstract -------- Abstract:For the first time, a method has recently become available for fast computation of near-best rational approximations on arbitrary sets in the real line or complex plane: the AAA algorithm (Nakatsukasa-Sete-T. 2018). We will present the algorithm and then demonstrate a number of applications, includingdetection of singularities, model order reduction, analytic continuation, functions of matrices, nonlinear eigenvalue problems, interpolation of equispaced data, smooth extension of multivariate real functions, extrapolation of ODE and PDE solutions into the complex plane, solution of Laplace problems, conformal mapping, Wiener-Hopf factorization. -- Indico :: Email Notifier https://events.dm.unipi.it/e/158

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Colloquio De Giorgi - Volker Mehrmann, Dirac and Lagrange structures in energy-based mathematical modeling 24/02/23, 16:00
by Fabio Durastante 01 Feb '23

01 Feb '23

We apologize in advance for cross-posting. ******************************************************************************** CENTRO DI RICERCA MATEMATICA "ENNIO DE GIORGI" ******************************************************************************** COLLOQUIO DE GIORGI Centro De Giorgi, Pisa, 24th February 2023 Aula Dini: 4.00 pm The event will take place in person. Volker Mehrmann Technische Universität Berlin Title:“Dirac and Lagrange structures in energy-based mathematical modeling” Abstract: Most real world dynamical systems consist of subsystems from different physical domains, modelled by partial-differential equations, ordinary differential equations, and algebraic equations, combined with input and output connections. To deal with such complex system, in recent years the class of dissipative port-Hamiltonian (pH) descriptor systems has emerged as a very successful modeling methodology. The main reasons are that the network based interconnection of pH systems is again pH, Galerkin projection in PDE discretization and model reduction preserve the pH structure and the physical properties are encoded in the geometric properties of the flow as well as the algebraic properties of the equations. Furthermore, dissipative pH system form a very robust representation under structured perturbations and directly indicate Lyapunov functions for stability analysis. Using global geometric and algebraic points of view, via Dirac and Lagrange spaces or manifolds, translations between different representations are presented. Characterizations are also derived when a general differential-algebraic system can be transformed into one of these structured representations. Numerical approaches for computing the structural information and the described transformations are derived and the results are demonstrated with some real world examples. Web site: http://www.crm.sns.it/course/6529/ <https://es.sonicurlprotection-fra.com/click?PV=2&MSGID=20230131222506106602…> Please note that for organizational purposes, registration <https://es.sonicurlprotection-fra.com/click?PV=2&MSGID=20230131222506106602…>is mandatory. CRM Secretariat Scuola Normale Superiore Piazza dei Cavalieri, 3 56126 Pisa, Italy

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[Indico] Dr Gianluca Ceruti, Robust numerical integrators for dynamical low-rank approximation, 15/12/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 14 Dec '22

14 Dec '22

Title: Robust numerical integrators for dynamical low-rank approximation, Speaker(s): Dr Gianluca Ceruti, École Polytechnique Fédérale de Lausanne, Date and time: 15 Dec 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: room Aula Magna (Dipartimento di Matematica). You can access the full event here: https://events.dm.unipi.it/e/138 Abstract -------- The discretization of time-dependent high-dimensional PDEs suffers from an undesired effect, the so-called curse of dimensionality: The amount of data to be stored and treated grows exponentially and exceeds standard capacity of common computational devices. In this setting, time dependent model order reductions techniques are desirable. In the present seminar, we present a broad overview on dynamical low-rank approximation together with recent developments on robust numerical integrators for it. Dynamical low-rank approximation for matrices is firstly presented, and a numerical integrator with two remarkable properties is introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we construct two equivalent extensions for tensors, multi-dimensional arrays, in Tucker format - a high-order generalization of the SVD decomposition for matrices. These extensions are proven to preserve the excellent qualities of the matrix integrator. Then, via a novel compact formulation of the Tucker integrator, we further extend the matrix and Tucker projector splitting integrators to the most general class of Tree Tensor Networks. Important examples belonging to this class and of interest for applications are given by (but not only restricted to) Tensor Trains.The present seminar is based upon joint works with Ch. Lubich, H. Walach, J. Kusch, and D. Sulz. -- Indico :: Email Notifier https://events.dm.unipi.it/e/138

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[Indico] Dr Gianluca Ceruti, Robust numerical integrators for dynamical low-rank approximation, 15/12/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 12 Dec '22

12 Dec '22

Title: Robust numerical integrators for dynamical low-rank approximation, Speaker(s): Dr Gianluca Ceruti, École Polytechnique Fédérale de Lausanne, Date and time: 15 Dec 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: room Aula Riunioni (Dipartimento di Matematica). You can access the full event here: https://events.dm.unipi.it/e/138 Abstract -------- The discretization of time-dependent high-dimensional PDEs suffers from an undesired effect, the so-called curse of dimensionality: The amount of data to be stored and treated grows exponentially and exceeds standard capacity of common computational devices. In this setting, time dependent model order reductions techniques are desirable. In the present seminar, we present a broad overview on dynamical low-rank approximation together with recent developments on robust numerical integrators for it. Dynamical low-rank approximation for matrices is firstly presented, and a numerical integrator with two remarkable properties is introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we construct two equivalent extensions for tensors, multi-dimensional arrays, in Tucker format - a high-order generalization of the SVD decomposition for matrices. These extensions are proven to preserve the excellent qualities of the matrix integrator. Then, via a novel compact formulation of the Tucker integrator, we further extend the matrix and Tucker projector splitting integrators to the most general class of Tree Tensor Networks. Important examples belonging to this class and of interest for applications are given by (but not only restricted to) Tensor Trains.The present seminar is based upon joint works with Ch. Lubich, H. Walach, J. Kusch, and D. Sulz. -- Indico :: Email Notifier https://events.dm.unipi.it/e/138

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Assegno di ricerca presso il Dipartimento di Matematica
by Leonardo Robol 23 Nov '22

23 Nov '22

Buongiorno, si è appena aperto un bando per un assegno di ricerca di 12 mesi presso il Dipartimento di Matematica (di Pisa), su fondi PNRR. La scadenza è il 21/12/22. Vi prego diffondere l'annuncio con chiunque possa essere interessato/a. https://bandi.unipi.it/public/Bandi/Detail/f2d456ca-5df1-4fcd-b95c-d16d0434…. A presto, -- Leonardo Robol.

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[Indico] Aaron Melman, Recent extensions of scalar and matrix polynomial properties and their interactions, 10/11/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 03 Nov '22

03 Nov '22

Title: Recent extensions of scalar and matrix polynomial properties and their interactions, Speaker(s): Aaron Melman, Santa Clara University, USA, Date and time: 10 Nov 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/114 Abstract -------- Several results for scalar polynomials are extended and then generalized to matrix polynomials. Among them are a directional version of Pellet's theorem for both scalarand matrix polynomials, which establishes an exclusion interval for the magnitudes of polynomial zeros or eigenvalues having a given argument, as well as results involving real polynomials with sign restrictions on their coefficients. The latter lead to exclusion sectorsfor polynomial eigenvalues. In addition, it is shown how new results can be obtained by embedding scalar polynomials into a matrix polynomial framework, and examples are given of how the interactionbetween scalar and matrix polynomials benefits both. If time (and interest) permits, an improvement of theorems by Hayashi and Hurwitz from the beginning of the twentiethcentury will be presented. These theorems concern the location of polynomial zeros when the coefficients exhibit certain sign patterns. -- Indico :: Email Notifier https://events.dm.unipi.it/e/114

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Seminario di oggi (Santolo Leveque)
by Leonardo Robol 24 Oct '22

24 Oct '22

Cari tutt*, vi ricordo il seminario di oggi di Santolo Leveque, alle 16.00: https://events.dm.unipi.it/event/113/ Al contrario di come era stato scritto nei primi avvisi, il seminario sarà in Aula Riunioni, e non in Aula Magna (nel caso aveste annotato l'aula tempo fa). A dopo! -- Leonardo Robol

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Workshop on Quasi-Newton methods
by Stefano Cipolla 23 Oct '22

23 Oct '22

Dear Colleagues, we are delighted to inform you that we are organizing the event "Workshop on Quasi-Newton methods" which will be held in Edinburgh, 9th Nov 2022, please see https://www.maths.ed.ac.uk/~gondzio/qNewton2022/home.html for more information. The workshop aims at promoting the exchange of ideas and to advance the state of the art in the area of Quasi-Newton methods. The *hybrid* workshop will consist of five invited presentations by selected leading researchers. Remote and in person participation are welcome. If you are willing to take part, please register (free of charge) at your earliest convenience, but not later than 31st Oct 2022, at the link https://forms.gle/bNccQ7mTAKhnJYNW6 Very Best Regards, Jacek, Stefano -- Stefano Cipolla Postdoctoral Research Associate School of Mathematics University of Edinburgh James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh, EH9 3FD email: scipolla(a)ed.ac.uk The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. Is e buidheann carthannais a th’ ann an Oilthigh Dhùn Èideann, clàraichte an Alba, àireamh clàraidh SC005336.

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[Indico] Santolo Leveque, A “matching strategy” for optimal control problems with PDEs as constraints, 24/10/2022, 16:00 Europe/Rome
by leonardo.robol＠unipi.it 18 Oct '22

18 Oct '22

Title: A “matching strategy” for optimal control problems with PDEs as constraints, Speaker(s): Santolo Leveque, Scuola Normale Superiore, Pisa, Date and time: 24 Oct 2022, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/113 Abstract -------- Saddle-point systems arise quite often in many areas of scientific computing. For instance, this type of system can be found in computational fluid dynamics, constrained optimization, finance, image reconstruction, and many more scientific applications. Due to their convenient structure and high dimensionality, preconditioned iterative methods are usually employed in order to solve this class of problems. By making use of saddle-point theory, one is able to derive optimal preconditioners for a general saddle-point system. However, the major drawback is that the cost of applying their inverse operator is almost as costly as inverting the original system. For this reason, one would rather find easy-to-invert approximation of the main blocks of the preconditioner considered.In this talk, we will present the “matching strategy” derived in [3] for approximating the Schur complement of a saddle-point system arsing from optimal control problems with PDE as constraints. We will mainly focus on time-dependent PDE, when employing a Crank–Nicolson discretization in time. After applying an optimize-then-discretize approach, one is faced with continuous first-order optimality conditions consisting of a coupled system of PDEs. After discretizing with Crank–Nicolson, one has to solve for a non-symmetric system. We apply a carefully tailored invertible transformation for symmetrizing the latter, and derive an ideal preconditioner by making use of saddle-point theory. The transformation is then employed within the preconditioner in order to derive optimal approximations of the (1,1)-block and of the Schur complement. We prove the latter through bounds on the eigenvalues, and test our solver against the widely-used preconditioner derived in [2] for the linear system arising from a backward Euler discretization in time. These demonstrate the effectiveness and robustness of our solver with respect to all the parameters involved in the problem considered.This talk is based on the work in [1].References[1] S. Leveque and J. W. Pearson, Fast Iterative Solver for the Optimal Control of Time-Dependent PDEs with Crank–Nicolson Discretization in Time, Numer. Linear Algebra Appl. 29, e2419, 2022.[2] J. W. Pearson, M. Stoll and A. J. Wathen, Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems, SIAM J. Matrix Anal. Appl. 33, 1126–1152, 2012.[3] J. W. Pearson and A. J. Wathen, A New Approximation of the Schur Complement in Preconditioners for PDE-Constrained Optimization, Numer. Linear Algebra Appl. 19, 816–829, 2012. -- Indico :: Email Notifier https://events.dm.unipi.it/e/113

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[Indico] Aaron Melman, Recent extensions of scalar and matrix polynomial properties and their interactions, 10/11/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 10 Oct '22

10 Oct '22

Title: Recent extensions of scalar and matrix polynomial properties and their interactions, Speaker(s): Aaron Melman, Santa Clara University, USA, Date and time: 10 Nov 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/114 Abstract -------- Several results for scalar polynomials are extended and then generalized to matrix polynomials. Among them are a directional version of Pellet's theorem for both scalarand matrix polynomials, which establishes an exclusion interval for the magnitudes of polynomial zeros or eigenvalues having a given argument, as well as results involving real polynomials with sign restrictions on their coefficients. The latter lead to exclusion sectorsfor polynomial eigenvalues. In addition, it is shown how new results can be obtained by embedding scalar polynomials into a matrix polynomial framework, and examples are given of how the interactionbetween scalar and matrix polynomials benefits both. If time (and interest) permits, an improvement of theorems by Hayashi and Hurwitz from the beginning of the twentiethcentury will be presented. These theorems concern the location of polynomial zeros when the coefficients exhibit certain sign patterns. -- Indico :: Email Notifier https://events.dm.unipi.it/e/114

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[Indico] Santolo Leveque, A “matching strategy” for optimal control problems with PDEs as constraints, 24/10/2022, 16:00 Europe/Rome
by fabio.durastante＠unipi.it 04 Oct '22

04 Oct '22

Title: A “matching strategy” for optimal control problems with PDEs as constraints, Speaker(s): Santolo Leveque, Scuola Normale Superiore, Pisa, Date and time: 24 Oct 2022, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/113 Abstract -------- Saddle-point systems arise quite often in many areas of scientific computing. For instance, this type of system can be found in computational fluid dynamics, constrained optimization, finance, image reconstruction, and many more scientific applications. Due to their convenient structure and high dimensionality, preconditioned iterative methods are usually employed in order to solve this class of problems. By making use of saddle-point theory, one is able to derive optimal preconditioners for a general saddle-point system. However, the major drawback is that the cost of applying their inverse operator is almost as costly as inverting the original system. For this reason, one would rather find easy-to-invert approximation of the main blocks of the preconditioner considered.In this talk, we will present the “matching strategy” derived in [3] for approximating the Schur complement of a saddle-point system arsing from optimal control problems with PDE as constraints. We will mainly focus on time-dependent PDE, when employing a Crank–Nicolson discretization in time. After applying an optimize-then-discretize approach, one is faced with continuous first-order optimality conditions consisting of a coupled system of PDEs. After discretizing with Crank–Nicolson, one has to solve for a non-symmetric system. We apply a carefully tailored invertible transformation for symmetrizing the latter, and derive an ideal preconditioner by making use of saddle-point theory. The transformation is then employed within the preconditioner in order to derive optimal approximations of the (1,1)-block and of the Schur complement. We prove the latter through bounds on the eigenvalues, and test our solver against the widely-used preconditioner derived in [2] for the linear system arising from a backward Euler discretization in time. These demonstrate the effectiveness and robustness of our solver with respect to all the parameters involved in the problem considered.This talk is based on the work in [1].References[1] S. Leveque and J. W. Pearson, Fast Iterative Solver for the Optimal Control of Time-Dependent PDEs with Crank–Nicolson Discretization in Time, Numer. Linear Algebra Appl. 29, e2419, 2022.[2] J. W. Pearson, M. Stoll and A. J. Wathen, Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems, SIAM J. Matrix Anal. Appl. 33, 1126–1152, 2012.[3] J. W. Pearson and A. J. Wathen, A New Approximation of the Schur Complement in Preconditioners for PDE-Constrained Optimization, Numer. Linear Algebra Appl. 19, 816–829, 2012. -- Indico :: Email Notifier https://events.dm.unipi.it/e/113

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Reading course (Randomized linear algebra -- starting October 2022)
by Leonardo Robol 28 Sep '22

28 Sep '22

Cari tutti, insieme a Fabio e Stefano abbiamo pensato di organizzare per questo semestre un "Reading course", dove i partecipanti potranno alternarsi a presentare risultati significativi di analisi numerica presi da articoli e/o capitoli di libri. L'idea è di avere degli incontri informali di durata maggiore rispetto ai seminari (2h), in cui chi presenta abbia il tempo di spiegare le cose con calma (magari approfondendo anche alla lavagna, o mostrando degli esperimenti numerici). Gli incontri sono aperti a tutti, e speriamo che possano essere di particolare utilità per dottorandi / studenti magistrali. L'argomento con cui vorremmo iniziare è "Randomized Linear Algebra", per poi continuare successivamente (ammesso che l'iniziativa abbia successo) con un tema scelto in base ai desideri di chi partecipa. Anche per questo semestre abbiamo selezionato gli articoli introduttivi da cui partire, ma poi potremo scegliere cosa approfondire in base alle preferenze dell'audience. Trovate maggiori informazioni sulla pagina web: https://numpi.dm.unipi.it/reading-course Invitiamo chi volesse partecipare a segnarsi sul Doodle per la prima sessione, programmata agli inizi di Ottobre: https://doodle.com/meeting/participate/id/eXoknmgd Segnatevi entro venerdì 09/09, in modo che poi possiamo scegliere la prima data, e pubblicizzare ulteriormente l'iniziativa. A presto, -- Leonardo.

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Annuncio Seminario di Matematica, Dr. Anna Weller (26.09.2022)
by Fabio Durastante 21 Sep '22

21 Sep '22

*Avviso Seminario di Matematica* Data: Monday, September 26, 2022 Ora: 16:15 - 17:15 Luogo: Aula Volterra, Normale Speaker: Anna Weller University of Cologne Titolo: *A spectral Galerkin method for the solution of reaction-diffusion equations on metric graphs* Abstract: Weinvestigateaspectralsolutionapproachforreaction-diffusionequationsongraphs interpretedastopologicalspace(metricgraphs).Ofspecialinterestisthenumerical computationofeigenfunctionsofthenegativesecondorderderivativeactingoneach edge.Remarkably,itispossibletogiveanexplicitcharacterizationoftheseeigenfunctions andcorrespondingeigenvalues.Moreover,forequilateralgraphs,wewillshow howtoefficientlycomputeanarbitrarylowerpartofthespectrumusingaveryuseful relationshiptothegraphLaplacianmatrixoftheunderlyingcombinatorialgraph. Finally,wecanusethebasisofeigenfunctionsinaGalerkinapproachtosolvevarious PDEsonmetricgraphs,wereweherefocusonreaction-diffusionequations.This problemismotivatedbyarecentcollaborationwiththeInstituteofGeophysicsand MeteorologyoftheUniversityofCologneonthemodelingofproteindistributionin Alzheimer’sdiseasetogetherwiththeUniversityHospitalCologne1.Partofmynumerical resultsarejointworkwithProf.Dr.MarkAinsworth(BrownUniversity)and withChong-SonDroege(UniversityofCologne). References [1]M.Ainsworth,A.Weller,AspectralGalerkinmethodforthesolutionofpartialdifferential equationsonmetricgraphs,inpreparation. [2]M.Ainsworth,A.Weller,AspectralGalerkinmethodforthesolutionofreaction-diffusion equationsonmetricgraphs,OberwolfachReports,WorkshopReport36,2021. [3]A.Kunoth,A.Weller,T.Yilmaz,Acomputationalbrainspheremodelforthesimulationof Alzheimer’sDisease.SnapshotsofmodernmathematicsfromOberwolfach,inpreparation. [4]A.Weller,G.N.Bischof,P.Schl̈uter,N.Richter,J.Dronse,̈O.Onur,J.Kukolja,B.Neu- maier,A.Kunoth,Y.Shao,T.vanEimeren,A.Drzezga,Findingnewcommunities:A principleofneuronalnetworkreorganizationinAlzheimersdisease.BrainConnectivity, 11(3):225-238,2021.DOI:10.1089/brain.2020.0889 ThisworkwassupportedbytheExcellenceInitiativeoftheUniversityofCologne

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[NOMADS] Seminar today by Emre Mengi
by Francesco Tudisco 19 Sep '22

19 Sep '22

Dear all, It is my great pleasure to invite you all to today’s NOMADS seminar by Emre Mengi<http://home.ku.edu.tr/~emengi/> from Koc University (Turkey), who will present recent work on the computation of the dominant poles of a transfer function of a descriptor system. The seminar will take place **today Sept 19 at 14:30 (CET) in GSSI’s Library (NOT the main lecture hall as previously announced). Remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09 Below you can find title and abstract. Hope to see you all later today! All the best, —Francesco Tudisco ====== Emre Mengi, Koc University, Istanbul, Turkey http://home.ku.edu.tr/~emengi/<https://www.google.com/url?q=http://home.ku.edu.tr/~emengi/&sa=D&source=cal…> Title: Large-Scale Estimation of the Dominant Poles of a Transfer Function Abstract: The dominant poles of the transfer function of a descriptor system provide important insight into the behavior of the system. They indicate the parts of the imaginary axis where the transfer function exhibits large norm. Moreover, the dominant poles and corresponding eigenvectors can be put in use to form a reduced-order approximation to the system. In the talk, I will describe a subspace framework to compute a prescribed number of dominant poles of a large-scale descriptor system. The framework applies Petrov-Galerkin projections to the original system, then computes the dominant poles of the projected small-scale system, for instance by the QZ algorithm, and expands the subspaces so that the projected system after the subspace expansion interpolates the original system at these dominant poles. I will explain why the subspace framework converges at a quadratic rate, and report numerical results illustrating the rapid convergence, and accuracy of the approach. For more information, please see: https://num-gssi.github.io/seminar/<https://www.google.com/url?q=https://num-gssi.github.io/seminar/&sa=D&sourc…> The seminar will take place in the Library, but remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09<https://www.google.com/url?q=https://us02web.zoom.us/j/89668910844?pwd%3DTm…> -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/DB6PR05MB32237075AF…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar today by Stefano Massei
by Francesco Tudisco 14 Sep '22

14 Sep '22

Dear all, It is my great pleasure to invite you all to today’s NOMADS seminar by Stefano Massei<https://sites.google.com/view/stefanomassei/home>, University of Pisa, who will present his recent work on fast parallel-in-time numerical integration of differential equations. The seminar will take place today, Sept 14, at 15:00 (CET) in GSSI’s Main Lecture Hall (the “red room”). Remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09 Below you can find title and abstract. Hope to see you all later today! All the best, –– Francesco Tudisco Associate Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io<https://ftudisco.gitlab.io/> Stefano Massei University of Pisa, Italy https://sites.google.com/view/stefanomassei/home<https://www.google.com/url?q=https://sites.google.com/view/stefanomassei/ho…> Title of the talk: Improved parallel-in-time integration via low-rank updates and interpolation Abstract: This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of parallel-in-time integration leading to a class of algorithms called ParaDiag. We develop and analyze two novel approaches for the numerical solution of such equations. Our first approach is based on the observation that the modification of these equations performed by ParaDiag in order to solve them in parallel has low rank. Building upon previous work on low-rank updates of matrix equations, this allows us to make use of tensorized Krylov subspace methods to account for the modification. Our second approach is based on interpolating the solution of the matrix equation from the solutions of several modifications. Both approaches avoid the use of iterative refinement needed by ParaDiag and related space-time approaches in order to attain good accuracy. In turn, our new approaches have the potential to outperform, sometimes significantly, existing approaches. This potential is demonstrated for several different types of PDEs. For more information, please see: https://num-gssi.github.io/seminar/<https://www.google.com/url?q=https://num-gssi.github.io/seminar/&sa=D&sourc…> The seminar will take place in the Main Lecture Hall, but remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09<https://www.google.com/url?q=https://us02web.zoom.us/j/89668910844?pwd%3DTm…> -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/DB6PR05MB32231F13C7…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Fwd: Corso sui metodi matematici per la scienza del clima - prof. M. Ghil
by Leonardo Robol 01 Jul '22

01 Jul '22

Cari tutti, vi inoltro l'avviso di un corso di dottorato che si terrà la settimana prossima, e che potenzialmente potrebbe essere di interesse per gli iscritti alla mailing list (anche solo come fonte di applicazioni interessanti/rilevanti). La frequenza è libera, e sarà mandato in streaming anche online. A presto! -- Leonardo. -------- Forwarded Message -------- From: Simona Guidotti <simona.guidotti(a)unipi.it> To: utenti(a)fields.dm.unipi.it Subject: [Utenti] Corso sui metodi matematici per la scienza del clima - prof. M. Ghil Date: Fri, 1 Jul 2022 13:21:09 +0200 > Comunico che lunedì 4 luglio si terrà la prima lezione del corso sui > "Metodi matematici per la scienza del clima" (prof. Michael Ghil). > > Troverete tutte le informazioni alle seguenti pagine: > > https://www.dm.unipi.it/phd/phd-courses/ > > https://clima.dm.unipi.it/2022/01/26/doctorate-course-mathematical-methods-… > > Saluti, > > Simona Guidotti > > _______________________________________________ > Utenti mailing list > Utenti(a)fields.dm.unipi.it > https://fields.dm.unipi.it/listinfo/utenti

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[NOMADS] seminar - Massimiliano Fasi
by Francesco Tudisco 22 Jun '22

22 Jun '22

Dear all, You are all invited to the next NOMADS seminar on low-precision numerical computations, which will be given by Massimiliano Fasi from Durham University on Friday June 24, 2022. The seminar will take place in the GSSI’s Library, but remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09 Below you can find the details about his talk. Looking forward to seeing you all on Friday! – Francesco Tudisco Massimiliano Fasi (Durham University, UK) https://www.durham.ac.uk/staff/massimiliano-fasi/ Title of the talk: CPFloat: A C Library for Emulating Low-Precision Arithmetic Abstract: Low-precision floating-point arithmetic can be simulated via software by executing each arithmetic operation in hardware and rounding the result to the desired number of significant bits. For IEEE-compliant formats, rounding requires only standard mathematical library functions, but handling subnormals, underflow, and overflow demands special attention, and numerical errors can cause mathematically correct formulae to behave incorrectly in finite arithmetic. Moreover, the ensuing algorithms are not necessarily efficient, as the library functions these techniques build upon are typically designed to handle a broad range of cases and may not be optimized for the specific needs of floating-point rounding algorithms. CPFloat is a C library that offers efficient routines for rounding arrays of binary32 and binary64 numbers to lower precision. The software exploits the bit level representation of the underlying formats and performs only low-level bit manipulation and integer arithmetic, without relying on costly library calls. In numerical experiments the new techniques bring a considerable speedup (typically one order of magnitude or more) over existing alternatives in C, C++, and MATLAB. To the best of our knowledge, CPFloat is currently the most efficient and complete library for experimenting with custom low-precision floating-point arithmetic available in any language. For more information, please see: https://num-gssi.github.io/seminar/ -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/DB6PR05MB322380D250…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Fwd: Fwd: PhD-positions at the University of Stuttgart
by Federico Poloni 13 Jun '22

13 Jun '22

Buongiorno, inoltro questo annuncio per alcuni posti di dottorato in "Numerical Analysis of domain decomposition methods" in caso conosciate qualche interessato. Federico -------- Messaggio Inoltrato -------- Oggetto: PhD-positions at the University of Stuttgart Data: Mon, 13 Jun 2022 09:03:26 +0000 Mittente: Stamm, Benjamin <best(a)acom.rwth-aachen.de> A: Benjamin.Stamm(a)ians.uni-stuttgart.de <Benjamin.Stamm(a)ians.uni-stuttgart.de> Dear colleagues, Please apologize for the mass mail. It is my pleasure to announce several openings for PhD-positions with my start at the University of Stuttgart this summer. I would be extremely grateful if you could forward this mail to interested students and post the attached flyers in your building. Of course, I will also diffuse it in a less analog manner, but I’d also like to do it the good old way ;-) Warm greetings, Ben Prof. Dr. Benjamin Stamm Applied and Computational Mathematics RWTH Aachen University Schinkelstraße 2, 52062 Aachen (Germany) Tel.: + 49 / 241 - 80 98672 (direct line) Tel.: + 49 / 241 - 80 98660 (secretary) e-mail: best(a)acom.rwth-aachen.de <mailto:best@acom.rwth-aachen.de> web: http://tinyurl.com/jv7h8n4

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Math colloquium today
by Francesco Tudisco 26 May '22

26 May '22

Dear all, Please note that there was a typo in the event reminder you received earlier today. The lecture by Stefano Serra-Capizzano will take place today at 15:00 in the Main Lecture Hall, not in the Auditorium! ============== GSSI, via F Crispi 7. Room: MLH. Date: 26 May at 15:00 Stefano Serra-Capizzano, University of Insubria The GLT class as a Generalized Fourier Analysis and applications Participation is also possible via the zoom link: https://us02web.zoom.us/j/89664583638?pwd=MTluRndSWUhoMG5VbU80Rlcydmg2dz09 <https://us02web.zoom.us/j/89664583638?pwd=MTluRndSWUhoMG5VbU80Rlcydmg2dz09> Abstract Recently, the class of Generalized Locally Toeplitz (GLT) sequences has been introduced as a generalization both of classical Toeplitz sequences and of variable coefficient differential operators and, for every sequence of the class, it has been demonstrated that it is possible to give a rigorous description of the asymptotic spectrum in terms of a function (the symbol) that can be easily identified. This generalizes the notion of a symbol for differential operators also of fractional type (discrete and continuous) or for Toeplitz sequences for which it is identified through the Fourier coefficients and is related to the classical Fourier Analysis. The GLT class has nice algebraic properties and indeed it has been proven that it is stable under linear combinations, products, and inversion when the sequence which is inverted shows a sparsely vanishing symbol (sparsely vanishing symbol = a symbol which vanishes at most in a set of zero Lebesgue measure). Furthermore, the GLT class virtually includes any approximation by local methods (Finite Difference, Finite Element, Isogeometric Analysis of partial differential equations (PDEs) and, based on this, we demonstrate that our results on GLT sequences can be used in a PDE setting in various directions. For more information, please see: https://indico.gssi.it/event/394/ — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io <https://ftudisco.gitlab.io/> -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/66E0C4A0-72B8-4B7C-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[Indico] [Event reminder] The GLT class as a Generalized Fourier Analysis and applications (26/05/2022, 15:00 Europe/Rome)
by francesco.tudisco＠gssi.it 26 May '22

26 May '22

Please note that the event "The GLT class as a Generalized Fourier Analysis and applications" will start on 26 May 2022, 15:00 (Europe/Rome). It will take place at GSSI (Rectorate-Building-Auditorium). You can access the full event here: https://indico.gssi.it/e/394 Description ----------- Stefano Serra-Capizzano University of Insubria, Italy http://scienze-como.uninsubria.it/serra/ Title of the talk: The GLT class as a Generalized Fourier Analysis and applications Abstract: Recently, the class of Generalized Locally Toeplitz (GLT) sequences has been introduced as a generalization both of classical Toeplitz sequences and of variable coefficient differential operators and, for every sequence of the class, it has been demonstrated that it is possible to give a rigorous description of the asymptotic spectrum in terms of a function (the symbol) that can be easily identified. This generalizes the notion of a symbol for differential operators also of fractional type (discrete and continuous) or for Toeplitz sequences for which it is identified through the Fourier coefficients and is related to the classical Fourier Analysis. The GLT class has nice algebraic properties and indeed it has been proven that it is stable under linear combinations, products, and inversion when the sequence which is inverted shows a sparsely vanishing symbol (sparsely vanishing symbol = a symbol which vanishes at most in a set of zero Lebesgue measure). Furthermore, the GLT class virtually includes any approximation by local methods (Finite Difference, Finite Element, Isogeometric Analysis of partial differential equations (PDEs) and, based on this, we demonstrate that our results on GLT sequences can be used in a PDE setting in various directions. Detailed PDF version of the abstract: HERE The seminar will take place in the Auditorium, but remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89664583638?pwd=MTluRndSWUhoMG5VbU80Rlcydmg2dz09 Note ---- Dear all, This is just a gentle reminder that this week's Math Colloquium will take place today at 3pm in the Main Auditorium. Looking forward to seeing you all there! Best, Paolo Antonelli, Marielle Simon, Francesco Tudisco and Francesco Viola -- Indico :: Email Notifier https://indico.gssi.it/e/394 -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/165354840854.1432.1…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar - Paolo Cifani
by Francesco Tudisco 24 May '22

24 May '22

Dear all, You are all invited to the following NOMADS seminar by Paolo Cifani, GSSI, which will take place Today at 13:45 in MLH and online via zoom at the following address: https://us02web.zoom.us/j/83830006962?pwd=SmI1MTVKRTllU3dBR01Ybko5bzBJdz09 <https://us02web.zoom.us/j/83830006962?pwd=SmI1MTVKRTllU3dBR01Ybko5bzBJdz09> Looking forward to seeing you all later! Nicola and Francesco ============== GSSI, via F Crispi 7. Room: MLH. Date: 24 May at 13:45 Paolo Cifani (GSSI) Geometric integration of Lie-Poisson flows on the sphere In this seminar I will touch upon the recent developments in structure-preserving (geometric) integration of Euler’s equations for two-dimensional incompressible flows. It has been known for half a century that the dynamics of incompressible ideal fluids in two dimensions can be understood as an evolution equation on the contangent bundle of the infinite-dimensional Lie group of symplectic dffeomorphisms. In particular, the vorticity equation constitutes a Lie-Poisson system characterized by an infinite number of first integrals, i.e. the integrated powers of vorticity. This set of constraints, absent in three dimensions, has profound effects on the energy transfer mechanisms across scales of motion. Yet, the construction of a numerical system which preserves this rich Poisson structure has been elusive. Most attempts either fail in fully preserving the geometric structure or have a high computational complexity. Here, I will show that, thanks to our recent advances, it possible to design a geometric integrator which embeds this fundamental principle of the continuum into the discrete system at a modest computational cost. The construction of such scheme, the main numerical algorithms and their parallelisation on modern supercomputing facilities will be discussed. Finally, an application to the spectrum of homogeneous two-dimensional turbulence will be illustrated. For more information, please see: https://num-gssi.github.io/seminar/ The seminar will take place in the Main Lecture Hall, but remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09 — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io <https://ftudisco.gitlab.io/> -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/5893E020-236E-481D-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[Indico] [Event reminder] The GLT class as a Generalized Fourier Analysis and applications (26/05/2022, 15:00 Europe/Rome)
by francesco.tudisco＠gssi.it 23 May '22

23 May '22

Please note that the event "The GLT class as a Generalized Fourier Analysis and applications" will start on 26 May 2022, 15:00 (Europe/Rome). It will take place at GSSI (Rectorate-Building-Auditorium). You can access the full event here: https://indico.gssi.it/e/394 Description ----------- Stefano Serra-Capizzano University of Insubria, Italy http://scienze-como.uninsubria.it/serra/ Title of the talk: The GLT class as a Generalized Fourier Analysis and applications Abstract: Recently, the class of Generalized Locally Toeplitz (GLT) sequences has been introduced as a generalization both of classical Toeplitz sequences and of variable coefficient differential operators and, for every sequence of the class, it has been demonstrated that it is possible to give a rigorous description of the asymptotic spectrum in terms of a function (the symbol) that can be easily identified. This generalizes the notion of a symbol for differential operators also of fractional type (discrete and continuous) or for Toeplitz sequences for which it is identified through the Fourier coefficients and is related to the classical Fourier Analysis. The GLT class has nice algebraic properties and indeed it has been proven that it is stable under linear combinations, products, and inversion when the sequence which is inverted shows a sparsely vanishing symbol (sparsely vanishing symbol = a symbol which vanishes at most in a set of zero Lebesgue measure). Furthermore, the GLT class virtually includes any approximation by local methods (Finite Difference, Finite Element, Isogeometric Analysis of partial differential equations (PDEs) and, based on this, we demonstrate that our results on GLT sequences can be used in a PDE setting in various directions. Detailed PDF version of the abstract: HERE The seminar will take place in the Auditorium, but remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89664583638?pwd=MTluRndSWUhoMG5VbU80Rlcydmg2dz09 Note ---- Dear all, It is our pleasure to invite you all to the next Math Colloquium on Thursday May 19 at 3pm in the Main Auditorium. The speaker will be Stefano Serra-Capizzano, from the University of Insubria (Como, Italy) with a talk on Generalized Fourier Analysis and Applications. We look forward to seeing you all there! Please feel free to share this announcement as you see fit. Best, Paolo Antonelli, Marielle Simon, Francesco Tudisco and Francesco Viola -- Indico :: Email Notifier https://indico.gssi.it/e/394 -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/165331080936.1432.1…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Reminder: Seminario 24/5, 15:00 - Andrew Wathen
by Leonardo Robol 23 May '22

23 May '22

Cari tutti, vi ricordo il Colloquio de Giorgi di domani 24/5 alle 15:00, che sarà tenuto da Andrew Wathen. https://www.crm.sns.it/course/6307/ La registrazione per partecipare (stando a quanto indicato sul sito e sul poster, che allego) è obbligatoria per poter partecipare in presenza. -- Leonardo Robol.

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Fwd: Fwd: Modern Techniques of Very Large Scale Optimization, Edinburgh, 19th - 20th May 2022
by Fabio Durastante 12 May '22

12 May '22

FYI -------- Messaggio Inoltrato -------- Oggetto: Fwd: Modern Techniques of Very Large Scale Optimization, Edinburgh, 19th - 20th May 2022 Data: Thu, 12 May 2022 17:14:04 +0100 Mittente: Stefano Cipolla <scipolla(a)ed.ac.uk> A: fabio.durastante(a)unipi.it ======================== Dear Colleagues, we are delighted to inform you that the workshop "Modern Techniques of Very Large Scale Optimization" will be held in Edinburgh, 19th - 20th May 2022; please see https://www.maths.ed.ac.uk/~gondzio/admm2020/home.html for more information. Although the capacity of in-person attendance is already reached we are happy for online participants to follow the talks. If you are interested and would like to attend the workshop online, then please register (free of charge) at your earliest convenience but not later than Friday 13th May. We will send you a Zoom link. Very Best regards, Jacek, Stefano, Filippo ======================== -- Stefano Cipolla Postdoctoral Research Associate School of Mathematics University of Edinburgh James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh, EH9 3FD email: scipolla(a)ed.ac.uk The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. Is e buidheann carthannais a th’ ann an Oilthigh Dhùn Èideann, clàraichte an Alba, àireamh clàraidh SC005336.

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Fwd: CENTRO DE GIORGI -- ANNOUNCEMENT -- COLLOQUIO DE GIORGI (24 May 2022)
by Fabio Durastante 12 May '22

12 May '22

*********************************************************************************** CENTRO DI RICERCA MATEMATICA "ENNIO DE GIORGI" ********************************************************************************** COLLOQUIO DE GIORGI Centro De Giorgi, Pisa, 24 May 2022 Aula Dini: 3.00 pm The event will take place in person. Andrew Wathen University of Oxford Title:“Numerical solutions methods for problems of PDE-constrained optimisation” Abstract:Since the advent of computers there has been interest in numerical methods for solving partial differential equations (PDE) problems---both methods of approximation and numerical linear algebra for the resulting sets of equations which are usually of very large dimension. Sometimes it is the solutions themselves that are of interest, but there is a significant class of problems where there is a design optimization criterion with physical constraints that are expressed in terms of PDEs; it is always the motion of fluids described by flow equations which provide the principal constraints when an engineer designs an aerodynamic structure with minimal drag and acceptable lift for example. In this talk I will consider numerical methods for such optimization problems with PDE constraints, in particular methods of iterative numerical linear algebra that render feasible the solution of such problems on advanced computers. Web site:http://www.crm.sns.it/course/6307/ <http://www.crm.sns.it/course/6307/> Please note that for organizational purposes, registration <http://www.crm.sns.it/event/493/registration.html>is mandatory. CRM Secretariat STG Puteano Centro di Ricerca Matematica "Ennio De Giorgi" Scuola Normale Superiore Piazza dei Cavalieri, 3 56126 Pisa, Italy

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Seminario di oggi (link)
by Leonardo Robol 05 May '22

05 May '22

Cari tutti/e, Il seminario di oggi sarà disponibile, oltre che in presenza, anche in streaming al solito link https://meetings.dm.unipi.it/b/leo-xik-xu4. A dopo, -- Leonardo Robol

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[Indico] Stefano Massei, Improved parallel-in-time integration via low-rank updates and interpolation, 05/05/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 04 May '22

04 May '22

Title: Improved parallel-in-time integration via low-rank updates and interpolation, Speaker(s): Stefano Massei, Università di Pisa, Date and time: 5 May 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/89 Abstract -------- This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of parallel-in-time integration leading to a class of algorithms called ParaDiag. We develop and analyze two novel approaches for the numerical solution of such equations. Our first approach is based on the observation that the modification of these equations performed by ParaDiag in order to solve them in parallel has low rank. Building upon previous work on low-rank updates of matrix equations, this allows us to make use of tensorized Krylov subspace methods to account for the modification. Our second approach is based on interpolating the solution of the matrix equation from the solutions of several modifications. Both approaches avoid the use of iterative refinement needed by ParaDiag and related space-time approaches in order to attain good accuracy. In turn, our new approaches have the potential to outperform, sometimes significantly, existing approaches. This potential is demonstrated for several different types of PDEs. -- Indico :: Email Notifier https://events.dm.unipi.it/e/89

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[Indico] Stefano Massei, Improved parallel-in-time integration via low-rank updates and interpolation, 05/05/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 27 Apr '22

27 Apr '22

Title: Improved parallel-in-time integration via low-rank updates and interpolation, Speaker(s): Stefano Massei, Università di Pisa, Date and time: 5 May 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/89 Abstract -------- This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of parallel-in-time integration leading to a class of algorithms called ParaDiag. We develop and analyze two novel approaches for the numerical solution of such equations. Our first approach is based on the observation that the modification of these equations performed by ParaDiag in order to solve them in parallel has low rank. Building upon previous work on low-rank updates of matrix equations, this allows us to make use of tensorized Krylov subspace methods to account for the modification. Our second approach is based on interpolating the solution of the matrix equation from the solutions of several modifications. Both approaches avoid the use of iterative refinement needed by ParaDiag and related space-time approaches in order to attain good accuracy. In turn, our new approaches have the potential to outperform, sometimes significantly, existing approaches. This potential is demonstrated for several different types of PDEs. -- Indico :: Email Notifier https://events.dm.unipi.it/e/89

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Ph.D. Course: An introduction to fractional calculus: fundamental ideas and numerics
by Fabio Durastante 27 Apr '22

27 Apr '22

Dear all, Monday 2 May we begin with the Ph.D. course "An introduction to fractional calculus: fundamental ideas and numerics" from 2.00 pm to 4.00 pm in the Aula Seminari. Find the latest information at: https://fdurastante.github.io/courses/introfracalculus.html#about The plan is to schedule the other lessons with those present that day. If there are people that wish to attend, but have difficulties being in person, please let me know at fabio.durastante(a)unipi.it and I'll try activating a streaming of the lecture. For any other question, feel free to write an E-mail. Best, Fabio Durastante

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[Indico] Raf Vandebril,
by leonardo.robol＠unipi.it 12 Apr '22

12 Apr '22

Title: Construction of a sequence of orthogonal rational functions, Speaker(s): Raf Vandebril, Department of Computer Science, KU Leuven, Date and time: 13 Apr 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/86 Abstract -------- Orthogonal polynomials are an important tool to approximate functions. Orthogonal rational functions provide a powerful alternative if the function of interest is not well approximated by polynomials. Polynomials orthogonal with respect to certain discrete inner products can be constructed by applying the Lanczos or Arnoldi iteration to appropriately chosen diagonal matrix and vector. This can be viewed as a matrix version of the Stieltjes procedure. The generated nested orthonormal basis can be interpreted as a sequence of orthogonal polynomials. The corresponding Hessenberg matrix, containing the recurrence coefficients, also represents the sequence of orthogonal polynomials. Alternatively, this Hessenberg matrix can be generated by an updating procedure. The goal of this procedure is to enforce Hessenberg structure onto a matrix which shares its eigenvalues with the given diagonal matrix and the first entries of its eigenvectors must correspond to the elements of the given vector. Plane rotations are used to introduce the elements of the given vector one by one and to enforce Hessenberg structure. The updating procedure is stable thanks to the use of unitary similarity transformations. In this talk rational generalizations of the Lanczos and Arnoldi iterations are discussed. These iterations generate nested orthonormal bases which can be interpreted as a sequence of orthogonal rational functions with prescribed poles. A matrix pencil of Hessenberg structure underlies these iterations. We show that this Hessenberg pencil can also be used to represent the orthogonal rational function sequence and we propose an updating procedure for this case. The proposed procedure applies unitary similarity transformations and its numerical stability is illustrated. -- Indico :: Email Notifier https://events.dm.unipi.it/e/86

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[Indico] Construction of a sequence of orthogonal rational functions,
by leonardo.robol＠unipi.it 05 Apr '22

05 Apr '22

Title: Construction of a sequence of orthogonal rational functions, Speaker(s): Raf Vandebril, Department of Computer Science, KU Leuven, Date and time: 13 Apr 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/86 Abstract -------- Orthogonal polynomials are an important tool to approximate functions. Orthogonal rational functions provide a powerful alternative if the function of interest is not well approximated by polynomials. Polynomials orthogonal with respect to certain discrete inner products can be constructed by applying the Lanczos or Arnoldi iteration to appropriately chosen diagonal matrix and vector. This can be viewed as a matrix version of the Stieltjes procedure. The generated nested orthonormal basis can be interpreted as a sequence of orthogonal polynomials. The corresponding Hessenberg matrix, containing the recurrence coefficients, also represents the sequence of orthogonal polynomials. Alternatively, this Hessenberg matrix can be generated by an updating procedure. The goal of this procedure is to enforce Hessenberg structure onto a matrix which shares its eigenvalues with the given diagonal matrix and the first entries of its eigenvectors must correspond to the elements of the given vector. Plane rotations are used to introduce the elements of the given vector one by one and to enforce Hessenberg structure. The updating procedure is stable thanks to the use of unitary similarity transformations. In this talk rational generalizations of the Lanczos and Arnoldi iterations are discussed. These iterations generate nested orthonormal bases which can be interpreted as a sequence of orthogonal rational functions with prescribed poles. A matrix pencil of Hessenberg structure underlies these iterations. We show that this Hessenberg pencil can also be used to represent the orthogonal rational function sequence and we propose an updating procedure for this case. The proposed procedure applies unitary similarity transformations and its numerical stability is illustrated. -- Indico :: Email Notifier https://events.dm.unipi.it/e/86

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Fwd: [Dipartimento.di] Seminar in Computational Mathematics - B.
by Federico Poloni 18 Mar '22

18 Mar '22

-------- Forwarded Message -------- Subject: [Dipartimento.di] Seminar in Computational Mathematics - B. Filipecki Date: Fri, 18 Mar 2022 13:40:32 +0100 From: Federico Poloni <federico.poloni(a)unipi.it> To: dipartimento(a)di.unipi.it Dear all, within the activities of the Computational Mathematics Lab, we are pleased to announce the following seminar. Title: Hierarchical Optimization of the Electrical Power Grid Speaker: Bartosz Filipecki, Department of Computer Science, University of Pisa Date/Time: Wednesday, 23 March 2022 17:00 Place: Aula Seminari Est, Dipartimento di Informatica Abstract: European electrical power networks operation is becoming more and more difficult due to increasing load and uncertainty associated with renewable energy sources. To address this problem, we consider a hierarchical approach to optimization of power grid operation. First, microgrid demand is aggregated to provide flexibility to the distribution system operator (DSO). At this stage, the optimal power flow problem (OPF) is solved in order to determine the flexibilities that can be made available to the transmission system operator (TSO). Afterwards, OPF is solved to determine the operation of the highest voltage grids, including additional constraints related to security and stability. The former provide protection against line failure, so that no blackout occurs. The latter make sure that the system does not deviate in the dynamic sense from the solution to the static OPF problem. The TSO level can also include Flexible Alternating-Current Transmission Systems Devices (FACTS). These provide us with advanced methods to control the power flow, but at a significant computational cost. After obtaining the solution, we propagate it back through the DSO level to the microgrids, which completes the framework. Everyone is welcome to attend, in person or on MS Teams: https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZGE3ZDcyOTItOTViMS00… Mauro Passacantando Federico Poloni -- --Federico Poloni Dipartimento di Informatica, Università di Pisa https://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143 ______________________________________________ Dipartimento.di mailing list Dipartimento.di(a)listgateway.unipi.it http://listgateway.unipi.it/mailman/listinfo/dipartimento.di

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[Indico] [Event reminder] Grassmann extrapolation for
by leonardo.robol＠unipi.it 17 Mar '22

17 Mar '22

Please note that the event "Grassmann extrapolation for Born-Oppenheimer Molecular Dynamics" will start on 18 Mar 2022, 11:00 (Europe/Rome). It will take place at Dipartimento di Matematica (Aula Magna). You can access the full event here: https://indico.cs.dm.unipi.it/e/76 Description ----------- Born-Oppenheimer Molecular Dynamics (BOMD) is a powerful, yet very demanding technique in computational quantum chemistry. Performing a BOMD simulation require, for each time step, to compute the energy and forces for a quantum mechanical system, which can also be embedded in a classical environment. When Density Functional Theory is used as a quantum mechanical model, the most time-consuming step for each energy/forces evaluation is the solution to the non-linear eigenvalue problem that stems from the discretization of the Kohn-Sham equations. Limiting the number of iterations required to achieve a satisfactory convergence of the procedure is therefore paramount to reduce the cost - and therefore extend the applicability - of such simulations. The most important factor in reducing the number of iteration is starting from a good guess, usually in the form of a one-body reduced density matrix. In a BOMD simulation it is possible to extrapolate information from previous steps into a new guess, however, this is not straightforward due to the nonlinear constraints that the density matrix must satisfy. In this contribution, we address this issue by performing the extrapolation on the tangent plane to the Grassmann manifold where the density is defined, by mapping the manifold to its tangent plane with a locally bijective map, which allows us to perform a linear extrapolation and then map the result back to the manifold, ensuring thus that all the physical properties of the density matrix are correctly enforced. Preliminary benchmark calculations show that the strategy is general and robust, and that even when using a naive linear extrapolation we obtain a strategy that outperforms the current state-of-the-art methods. Streaming link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 -- Indico :: Email Notifier https://indico.cs.dm.unipi.it/e/76

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[Indico] [Event reminder] Grassmann extrapolation for
by leonardo.robol＠unipi.it 08 Mar '22

08 Mar '22

Please note that the event "Grassmann extrapolation for Born-Oppenheimer Molecular Dynamics" will start on 18 Mar 2022, 11:00 (Europe/Rome). It will take place at Dipartimento di Matematica (Aula Magna). You can access the full event here: https://indico.cs.dm.unipi.it/e/76 Description ----------- Born-Oppenheimer Molecular Dynamics (BOMD) is a powerful, yet very demanding technique in computational quantum chemistry. Performing a BOMD simulation require, for each time step, to compute the energy and forces for a quantum mechanical system, which can also be embedded in a classical environment. When Density Functional Theory is used as a quantum mechanical model, the most time-consuming step for each energy/forces evaluation is the solution to the non-linear eigenvalue problem that stems from the discretization of the Kohn-Sham equations. Limiting the number of iterations required to achieve a satisfactory convergence of the procedure is therefore paramount to reduce the cost - and therefore extend the applicability - of such simulations. The most important factor in reducing the number of iteration is starting from a good guess, usually in the form of a one-body reduced density matrix. In a BOMD simulation it is possible to extrapolate information from previous steps into a new guess, however, this is not straightforward due to the nonlinear constraints that the density matrix must satisfy. In this contribution, we address this issue by performing the extrapolation on the tangent plane to the Grassmann manifold where the density is defined, by mapping the manifold to its tangent plane with a locally bijective map, which allows us to perform a linear extrapolation and then map the result back to the manifold, ensuring thus that all the physical properties of the density matrix are correctly enforced. Preliminary benchmark calculations show that the strategy is general and robust, and that even when using a naive linear extrapolation we obtain a strategy that outperforms the current state-of-the-art methods. Streaming link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 -- Indico :: Email Notifier https://indico.cs.dm.unipi.it/e/76

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Annunci di seminari NumPI
by Leonardo Robol 08 Mar '22

08 Mar '22

Cari tutti, d'ora in poi -ammesso che la cosa funzioni bene- useremo la piattaforma Indico per inviare gli annunci dei seminari sulla mailing list, dato che lo fa in automatico (reminder inclusi, cosa che io tendo a dimenticare piuttosto facilmente). A breve dovrebbe arrivarne uno. Il formato dell'annuncio sarà leggermente diverso rispetto al solito, ma si tratta sempre dei seminari NumPi. A presto, -- Leonardo.

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Seminar announcement
by Fabio Durastante 07 Mar '22

07 Mar '22

Speaker: Nicola Guglielmi Affiliation: Gran Sasso Science Institute Venue: Aula Volterra, Scuola Normale Superiore *Remark. *Il seminario si terrà in presenza. Chi fosse interessato a partecipare deve scrivere a classi(a)sns.it _entro le 9:00 di Lunedì __ __7 marzo 2022_ *Abstract. *Stability and robustness analysis of linear continuous and discrete dynamical systems is a vast and active interdisciplinary research area. Although the word stability is used in many different contexts, in this talk it is meant to indicate the broad spectrum of issues that arise in the analytical and numerical study of dynamical and control systems, especially in relation to qualitative information of the system under study. These issues result from the need to develop stable and reliable systems robustly preserving essential qualitative properties. The analysis of these features is often based on eigenvalue optimization or on pseudospectral measures of a certain matrix A, where the structure of A (e.g., sparse, Hamiltonian, nonnegative, Toeplitz, etc.) plays an important role. The main goal of this talk is to show how these structured distances can be approximated. The proposed method is a two-level iterative algorithm, where in an inner iteration a gradient flow drives perturbations to the original matrix of a fixed size into a minimum of a functional that depends on eigenvalues (and possibly eigenvectors), and in an outer iteration the perturbation size is optimized such that the functional reaches some target value (for example O). An interesting point - related to certain low-rank properties of extremizers - lies in the possibility of considering gradient flows on low-rank manifolds. The talk is mainly inspired by joint works with Christian Lubich (Tuebingen). Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar announcement
by Fabio Durastante 23 Feb '22

23 Feb '22

Speaker: Leonardo Robol Affiliation: Università di Pisa Venue: Aula Magna, Dipartimento di Matematica Time: Thursday, 24/02/2022, 11:00 Title: Sampling the eigenvalues of random matrices Random matrices (that is, matrices with random variables as entries) appear in several areas of mathematics and physics. Often, one is interested in sampling their eigenvalues (which are again random variables); we briefly recap the main tools that can be used to sample the joint eigenvalue distribution for Hermitian matrices from the Gaussian unitary Ensemble (GUE) with O(n^2) flops, and discuss how similar ideas can be used to efficiently perform the analogous operation for Haar-distributed orthogonal or unitary matrices. The latter operation requires to find a suitable compact canonical form for upper Hessenberg unitary matrices obtained by reducing random orthogonal/unitary matrices, and then efficiently operate on this compact representation to compute the eigenvalues. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Annuncio di seminario 10/02
by Fabio Durastante 10 Feb '22

10 Feb '22

Speaker: Milo Viviani Affiliation: Scuola Normale Superiore Venue: Aula Magna, Dipartimento di Matematica Time: Thursday, 10/02/2022, 11:00 Title:Solving cubic matrix equations arising in conservative dynamics Spatial semi-discretization of conservative PDEs can be described as flows in suitable matrix spaces, which in turn leads to the need to solve polynomial matrix equations, a classical and important topic both in theoretical and in applied mathematics. Solving these equations numerically is challenging due to the presence of several conservation laws which our finite models incorporate and which must be retained while integrating the equations of motion. In the last thirty years, the theory of geometric integration has provided a variety of techniques to tackle this problem. These numerical methods require to solve both direct and inverse problems in matrix spaces. We present two algorithms to solve a cubic matrix equation arising in the geometric integration of isospectral flows. This type of ODEs includes finite models of ideal hydrodynamics, plasma dynamics, and spin particles, which we use as test problems for our algorithms. Meeting link:https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Corso di dottorato: Low-rank approximation techniques for matrices
by Leonardo Robol 14 Jan '22

14 Jan '22

Buongiorno, segnalo il corso di dottorato "Low rank approximation techniques for matrices and tensors", che sarà tenuto a partire del prossimo 7 febbraio da Stefano Massei presso il dipartimento di Informatica. È un corso concentrato in 3 settimane; in quel periodo Stefano sarà ospite del Dipartimento di Matematica. Riporto qui sotto ulteriori informazioni, che in ogni caso trovate sulla pagina web del corso di dottorato in Computer Science [1]. ===================================================================== Low rank approximation techniques for matrices and tensors Lecturers: Stefano Massei (TU/e, The Netherlands) Period: From February 7th to February 26th, 2022 Schedule: 6 hours the first and second week, 4 hours the third week To attend the course send an email to s.massei(a)tue.nl Matrices and tensors are the heart of many scientific and industrial computational problems. In this course we will survey numerical methods that leverage low-rank structures in matrices and tensors in order to reduce the consumption of computational resources while maintaining a satisfactory accuracy. The course will touch the following topics: * Low-rank tensor formats: Tucker and tensor train * Deterministic and randomized algorithms for low-rank approximation of matrices and tensors * Trace and diagonal estimation of black box matrices [1] https://dottorato.di.unipi.it/phd-programme/teaching/phd-courses-a-y-2021-2…

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Spostamento mailing list
by Leonardo Robol 09 Dec '21

09 Dec '21

Cari tutti, stiamo provando a spostare la mailing list NumPi su un nuovo server, per permettere anche ai non-unipi di iscriversi in autonomia. Per ora è un tentativo sperimentale, ma se leggete questo messaggio è già un buon segno; l'indirizzo a cui scrivere cambia, e diventa numpi(a)lists.dm.unipi.it. Se vediamo che tutto va bene, faremo puntare il vecchio alias (numpi(a)di.unipi.it) a questo nuovo indirizzo, in modo che il passaggio sia il più indolore possibile. Le vecchie iscrizioni e preferenze sono state importate; segnalatemi pure ogni problema che doveste notare! A presto, -- Leonardo Robol.

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Annuncio di seminario, 6/12 (Bruno Iannazzo)
by Leonardo Robol 02 Dec '21

02 Dec '21

Speaker: Bruno Iannazzo Affiliation: Università degli studi di Perugia Venue: Aula Magna, Dipartimento di Matematica Time: Lunedì, 6/12/2021, 15:00 Title: New geometries on positive-definite matrices and their relation to the power means We introduce a new family of geometries on the cone of positive definite matrices obtained from the Hessian of the power potential and provide explicit expressions for related quantities such as geodesics and distances. This generalizes in some sense the geometry obtained from the Hessian of the logarithmic potential, whose geodesic has been understood as the weighted geometric mean of two matrices. Indeed, the new geometries provide a definition of matrix power mean alternative to the existing ones. We discuss some properties of the proposed power mean and relate it with the geometric mean. Finally, we discuss on how these geometries can be used to accelerate the convergence of optimization algorithms for the matrix geometric mean of several variables. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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[NOMADS] Seminar - Matthew Colbrook - Dec 1 at 17:00
by Francesco Tudisco 29 Nov '21

29 Nov '21

Dear all, We are starting this week a new series of NOMADS seminars on Numerical methods, Matrix analysis and Data Science. This week's seminar will take place on *Wednesday December 1 at 17:00* (CET) in the *GSSI Main Lecture Hall* (the "red" conference hall by the entrance of the lecture rooms building). The speaker is Matthew J Colbrook from University of Cambridge and ENS Paris, with a talk on the computation of semigroups of fractional PDEs. Title and abstract are below. In person participation is encouraged, but remote attendance will also be possible via the link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09 Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Hope to see you all on Wednesday! And, please feel free to distribute this announcement as you see fit. Francesco and Nicola ----------- Title: Computing semigroups and time-fractional PDEs with error control Abstract: We develop an algorithm that computes strongly continuous semigroups on infinite-dimensional Hilbert spaces with explicit error control. Given a generator $A$, a time $t > 0$, an arbitrary initial vector $u_0$ and an error tolerance $\epsilon > 0$, the algorithm computes $\exp(tA)u_0$ with error bounded by $\epsilon$. The (parallelisable) algorithm is based on a combination of a regularized functional calculus, suitable contour quadrature rules and the adaptive computation of resolvents in infinite dimensions. As a particular case, we deal with semigroups on $L^2(R^d)$ that are generated by partial differential operators with polynomially bounded coefficients of locally bounded total variation. For analytic semigroups, we provide a quadrature rule whose error decreases like $\exp(−cN/ log(N))$ for $N$ quadrature points, that remains stable as $N \to \infty$, and which is also suitable for infinite-dimensional operators. Finally, we extend the method to time-fractional PDEs (where it avoids singularities as $t \to 0$ and large memory consumption). Numerical examples are given, including: Schrödinger and wave equations on the aperiodic Ammann–Beenker tiling and fractional beam equations arising in the modelling of small-amplitude vibration of viscoelastic materials. The spectral analysis (which is always needed for contour methods) is considerably simplified due to an infinite-dimensional “solve-then-discretise” approach. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/CAO2_FWmWATOjsjz5v5…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Annuncio di seminario, 19/11 (Mariarosa Mazza)
by Leonardo Robol 18 Nov '21

18 Nov '21

Speaker: Mariarosa Mazza Affiliation: Università dell'Insubria Venue: Aula Magna, Dipartimento di Matematica Time: Venerdì, 19/11/2021, 10:00 Title: Caputo and Riemann-Liouville fractional derivatives: a matrix comparison Fractional derivatives are a mathematical tool that received much attention in the last decades because of their non-local behavior which has been demonstrated to be useful when modeling anomalous diffusion phenomena appearing, e.g., in imaging or electrophysiology. Two of the most famous definitions of fractional derivatives are the Riemann- Liouville and the Caputo ones. The two formulations are related by a well-known formula that expresses a Riemann-Liouville derivative as a Caputo one plus a term that depends on the function and its derivatives at the boundary. As a consequence of this relation, Riemann-Liouville and Caputo derivatives coincide only for sufficiently smooth functions that satisfy homogeneous conditions at the boundary. Aiming at uncovering how much this discrepancy reflects on their discretized counterparts, we focus on the relation between Riemann-Liouville and Caputo derivatives once approximated by a collocation method based on B-splines, i.e., high order finite elements with maximum regularity. We show that when the fractional order α ranges in (1,2) their difference in terms of matrices corresponds to a rank-1 correction whose spectral norm increases with the mesh-size n and is o(√n). On one hand, this implies that the spectral distribution for the B-spline collocation matrices corresponding to the Riemann-Liouville and Caputo derivatives coincide; on the other hand, the presence of the rank-1 correction makes the Caputo matrices worse conditioned for α tending to 1 due to a larger maximum singular value. Some linear algebra consequences of all this knowledge are discussed, and a selection of numerical experiments that validate our findings is provided together with a numerical study of the approximation behavior of B-spline collocation. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Annuncio di seminario, 25/10 (Cecilia Pagliantini)
by Leonardo Robol 25 Oct '21

25 Oct '21

Speaker: Cecilia Pagliantini Affiliation: TU Eindhoven Venue: Sala Seminari, Dipartimento di Matematica Time: Monday, 25/10/2021, 15:00 Title: Structure-preserving dynamical model order reduction of parametric Hamiltonian systems In real-time and many-query simulations of parametric differential equations, computational methods need to face high computational costs to provide sufficiently accurate and stable numerical solutions. To address this issue, model order reduction techniques aim at constructing low-complexity high-fidelity surrogate models that allow rapid and accurate solutions under parameter variation. In this talk, we will consider reduced basis methods (RBM) for the model order reduction of parametric Hamiltonian dynamical systems describing nondissipative phenomena. The development of RBM for Hamiltonian systems is challenged by two main factors: (i) failing to preserve the geometric structure encoding the physical properties of the dynamics, such as invariants of motion or symmetries, might lead to instabilities and unphysical behaviors of the resulting approximate solutions; (ii) the \emph{local} low-rank nature of transport-dominated and nondissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations. We will discuss how to address these aspects via a structure-preserving nonlinear reduced basis approach based on dynamical low-rank approximation. The gist of the proposed method is to evolve low-dimensional surrogate models on a phase space that adapts in time while being endowed with the geometric structure of the full model. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Annuncio di seminario, 15/10 (Igor Simunec)
by Leonardo Robol 15 Oct '21

15 Oct '21

Cari tutti, a breve ricominceremo con i tradizionali seminari NumPi, questa volta in forma "ibrida". Per tutti quelli che vorranno ci sarà la possibilità di seguire in presenza in Aula Magna del Dipartimento di Matematica (compilando questa form: https://forms.gle/AaMgajhKhroXdHqY6) Per gli altri, organizzeremo lo streaming tramite il solito link ( https://hausdorff.dm.unipi.it/b/leo-xik-xu4) Qui sotto trovate l'annuncio del primo seminario; a breve vi farò avere un Doodle per provare a scegliere un giorno che torni il più comodo possibile a tutti, da utilizzare per quelli successivi. Trovate tutte le informazioni sulla pagina dei seminari del sito NumPi (https://numpi.dm.unipi.it/seminars) A presto, -- Leonardo. Speaker: Igor Simunec Affiliation: Scuola Normale Superiore, Pisa Time: Friday, 15/10/2021, 16:30 Title: Computation of generalized matrix functions with rational Krylov methods Generalized matrix functions [3] are an extension of the notion of standard matrix functions to rectangular matrices, defined using the singular value decomposition instead of an eigenvalue decomposition. In this talk, we consider the computation of the action of a generalized matrix function on a vector and we present a class of algorithms based on rational Krylov methods [2]. These algorithms incorporate as a special case previous methods based on the Golub-Kahan bidiagonalization [1]. By exploiting the quasiseparable structure of the projected matrices, we show that the basis vectors can be updated using a short recurrence, which can be seen as a generalization to the rational case of the Golub-Kahan bidiagonalization. We also prove error bounds that relate the error of these methods to uniform rational approximation on an interval containing the singular values of the matrix. The effectiveness of the algorithms and the accuracy of the bounds is illustrated with numerical experiments. This is joint work with Angelo A. Casulli (Scuola Normale Superiore). [1] F. Arrigo, M. Benzi, and C. Fenu, Computation of generalized matrix functions, SIAM J. Matrix Anal. Appl. 37 (2016), no. 3, 836–860. [2] A. A. Casulli, I. Simunec, Computation of generalized matrix functions with rational Krylov methods, arXiv:2107.12074 (2021). [3] J. B. Hawkins and A. Ben-Israel, On generalized matrix functions, Linear and Multilinear Algebra 1 (1973), no. 2, 163–171. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Orario per seminari NumPi
by Leonardo Robol 13 Oct '21

13 Oct '21

Cari tutti, a partire dal prossimo seminario (dopo quello di Igor venerdì) cercheremo di scegliere un orario compatibile con gli impegni di tutti, e mantere una cadenza indicativamente bisettimanale. Ho creato un Doodle [1] per la settimana 25/10 - 29/10, dove chiederei (a chi è interessato a seguire i seminari in presenza e/o online) di indicare le preferenze di orario. Sebbene il Doodle sia per quella settimana specifica, è da intendersi come le preferenze in base ai vostri impegni settimanali. Vi chiederei di farci avere una risposta entro venerdì, così che possiamo organizzare il seminario seguente basandoci sulle risposte. Grazie! A presto, -- Leonardo (e Fabio). [1] https://doodle.com/poll/dtvyu6uakv3exdp8

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PhD position in Prague
by Leonardo Robol 12 Aug '21

12 Aug '21

Cari tutti, inoltro un messaggio da Stefano Pozza, su una borsa di dottorato disponibile alla Charles University, Praga. Trovate i dettagli in fondo alla mail. Buone vacanze, -- Leonardo. ----------------------------------------------------------------------- Ph.D. Position, Dep Num Math, Charles Univ, Czech Rep A Ph.D. position is available within the framework of the Primus Research Programme: "A Lanczos-like Method for the Time-Ordered Exponential" at the Faculty of Mathematics and Physics, Charles University, Prague. The four years of Ph.D. studies will take place in the Department of Numerical Mathematics under the supervision of Dr. Stefano Pozza (PI of the project). The department offers an international environment at one of the top universities in the Czech Republic, and the oldest university in Central Europe. The student will also have the opportunity to work with external collaborators from France, Italy, and the UK. The applicants must hold a Master's degree by the start date of Spring 2022 (to be announced) and have a strong interest in numerical linear algebra and numerical analysis. Knowledge of Matlab or other programming languages is necessary. Applicants will have to prove their English language level by passing an exam (it is possible to waive the examination under some conditions). Application deadline: September 30, 2021. More information and application instructions: https://www.starlanczos.cz/open-positions

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Cena NumPi
by Leonardo Robol 30 Jun '21

30 Jun '21

Cari tutti, come gli anni scorsi (ed in particolare quelli non-pandemici), vorremmo provare ad organizzare una cena di "fine seminari"; più che altro sarebbe una scusa per vedersi, a maggior ragione quest'anno dove non ci siamo (quasi) mai incontrati di persona. Ho predisposto un Doodle dove potete segnare la vostra disponibilità, se intendete partecipare: https://doodle.com/poll/z2xw2k6u5zzfybn3 Siete tutti benvenuti (dagli ordinari ai dottorandi, ma anche simpatizzanti, ecc.). Vi chiederei solo di segnare la vostra presenza quanto prima così che riusciamo ad organizzarci per bene. Il luogo non è stato ancora scelto, ma proposte sono sempre bene accette; probabilmente dovremo scegliere anche in funzione del numero di partecipanti. A presto! -- Leonardo Robol.

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Reminder: Seminar today (Stefano Cipolla)
by Fabio Durastante 18 Jun '21

18 Jun '21

Speaker: Stefano Cipolla Affiliation: University of Edinburgh Time: Friday, 18/06/2021, 16:00 Title: Random multi-block ADMM: an ALM based view for the QP case Because of its wide versatility and applicability in multiple fields, the n-block alternating direction method of multipliers (ADMM) for solving nonseparable convex minimization problems, has recently attracted the attention of many researchers [1, 2, 4]. When the n-block ADMM is used for the minimization of quadratic functions, it consists in a cyclic update of the primal variables xi for i = 1,...,n in the Gauss-Seidel fashion and a dual ascent type update of the dual variable μ. Despite the fact the connections between ADMM and Gauss-Seidel are quite well known, to the best of our knowledge, an analysis from the purely numerical linear algebra point of view is lacking in literature. Aim of this talk is to present a series of very recent results obtained on this topic which shed further light on basic issues as convergence and efficiency [3]. [1] Chen, C., Li, M., Liu, X., Ye, Y. (2019). Extended ADMM and BCD for nonseparable convex minimization models with quadratic coupling terms: convergence analysis and insights. Mathematical Programming, 173(1-2), 37-77. [2] Chen, C., He, B., Ye, Y., Yuan, X. (2016). The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent. Mathematical Programming, 155(1-2), 57-79. [3] Cipolla, S., Gondzio, J (2020). ADMM and inexact ALM: the QP case. arXiv 2012.09230. [4] Sun, R., Luo, Z. Q., Ye, Y. (2020). On the efficiency of random permutation for ADMM and coordinate descent. Mathematics of Operations Research, 45(1), 233-271. https://www.dm.unipi.it/webnew/it/seminari/random-multi-block-admm-alm-base… <https://www.dm.unipi.it/webnew/it/seminari/random-multi-block-admm-alm-base…> Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 <https://hausdorff.dm.unipi.it/b/leo-xik-xu4>

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Colloquium on 16/06 at 5pm (Volker Mehrmann)
by Paola Boito 16 Jun '21

16 Jun '21

Dear all, An online colloquium of the Department of Mathematics at UniPi is planned on June 16 at 17:00. You are all welcome! The speaker is Volker Mehrmann (TU Berlin). Title: Energy based modeling, simulation, and control. Mathematical theory and algorithms for the solution of real world problems. Abstract: Energy based modeling via port-Hamiltonian systems is a relatively new paradigm in all areas of science and engineering. These systems have wonderful mathematical properties, concerning their analytic, geometric and algebraic properties, but also with respect to their use in numerical algorithms for space-time discretization, model reduction and control. We will introduce the model class and their mathematical properties and we illustrate their usefulness with several real world applications. Google Meet link: https://meet.google.com/qii-tcks-rrr

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Seminar on 18/06 (Stefano Cipolla)
by Leonardo Robol 14 Jun '21

14 Jun '21

Speaker: Stefano Cipolla Affiliation: University of Edinburgh Time: Friday, 18/06/2021, 16:00 Title: Random multi-block ADMM: an ALM based view for the QP case Because of its wide versatility and applicability in multiple fields, the n-block alternating direction method of multipliers (ADMM) for solving nonseparable convex minimization problems, has recently attracted the attention of many researchers [1, 2, 4]. When the n-block ADMM is used for the minimization of quadratic functions, it consists in a cyclic update of the primal variables xi for i = 1,...,n in the Gauss-Seidel fashion and a dual ascent type update of the dual variable μ. Despite the fact the connections between ADMM and Gauss-Seidel are quite well known, to the best of our knowledge, an analysis from the purely numerical linear algebra point of view is lacking in literature. Aim of this talk is to present a series of very recent results obtained on this topic which shed further light on basic issues as convergence and efficiency [3]. [1] Chen, C., Li, M., Liu, X., Ye, Y. (2019). Extended ADMM and BCD for nonseparable convex minimization models with quadratic coupling terms: convergence analysis and insights. Mathematical Programming, 173(1-2), 37-77. [2] Chen, C., He, B., Ye, Y., Yuan, X. (2016). The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent. Mathematical Programming, 155(1-2), 57-79. [3] Cipolla, S., Gondzio, J (2020). ADMM and inexact ALM: the QP case. arXiv 2012.09230. [4] Sun, R., Luo, Z. Q., Ye, Y. (2020). On the efficiency of random permutation for ADMM and coordinate descent. Mathematics of Operations Research, 45(1), 233-271. https://www.dm.unipi.it/webnew/it/seminari/random-multi-block-admm-alm-base… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Math Colloquium - Lars Ruthotto - June 17 at 17:00
by Francesco Tudisco 14 Jun '21

14 Jun '21

Dear all, the next GSSI Math Colloquium will be held on *Thursday June 17 at 5pm* (please note **the time is *5pm* instead of the usual 3pm**). The speaker is Lars Ruthotto, with a lecture connecting numerical methods for differential equations and deep learning architectures. More details below. Lars Ruthotto is Associate Professor of Mathematics and Computer Science at Emory University (Atlanta, USA). To attend the talk please use to the following Zoom link: https://us02web.zoom.us/j/85179454721?pwd=TjA0V2M3L3lVTk1NNEdVcGpQcXlTdz09 Please feel free to distribute this announcement as you see fit. Looking forward to seeing you all on Thursday! Paolo Antonelli, Stefano Marchesani, Francesco Tudisco and Francesco Viola --------------------- Title: Numerical Methods for Deep Learning motivated by Partial Differential Equations Abstract: Understanding the world through data and computation has always formed the core of scientific discovery. Amid many different approaches, two common paradigms have emerged. On the one hand, primarily data-driven approaches—such as deep neural networks—have proven extremely successful in recent years. Their success is based mainly on their ability to approximate complicated functions with generic models when trained using vast amounts of data and enormous computational resources. But despite many recent triumphs, deep neural networks are difficult to analyze and thus remain mysterious. Most importantly, they lack the robustness, explainability, interpretability, efficiency, and fairness needed for high-stakes decision-making. On the other hand, increasingly realistic model-based approaches—typically derived from first principles and formulated as partial differential equations (PDEs)—are now available for various tasks. One can often calibrate these models—which enable detailed theoretical studies, analysis, and interpretation—with relatively few measurements, thus facilitating their accurate predictions of phenomena. In this talk, I will highlight recent advances and ongoing work to understand and improve deep learning by using techniques from partial differential equations. I will demonstrate how PDE techniques can yield better insight into deep learning algorithms, more robust networks, and more efficient numerical algorithms. I will also expose some of the remaining computational and numerical challenges in this area. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io <https://ftudisco.gitlab.io> -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/51fd86c2-9ac2-482f-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Seminar on 04/06 (Margherita Porcelli)
by Leonardo Robol 04 Jun '21

04 Jun '21

Speaker: Margherita Porcelli Affiliation: Università di Bologna Time: Friday, 04/06/2021, 16:00 Title: Relaxed Interior point methods for low-rank semidefinite programming problems In this talk we will discuss a relaxed variant of interior point methods for semidefinite programming problems (SPDs). We focus on problems in which the primal variable is expected to be low-rank at optimality. Such situations are common in relaxations of combinatorial optimization problems, for example in maximum cut problems as well as in matrix completion problems. We exploit the structure of the sought solution and relax the rigid structure of IPMs for SDP. In anticipation to converging to a low-rank primal solution, a special nearly low-rank form of all primal iterates is imposed. To accommodate such a (restrictive) structure, the first order optimality conditions have to be relaxed and are therefore approximated by solving an auxiliary least-squares problem. The relaxed interior point framework opens numerous possibilities how primal and dual approximated Newton directions can be computed. In particular, it admits the application of both the first- and the second-order methods in this context. In this talk we will focus on second-order approaches and discuss the difficulties arising in the linear algebra phase. A prototype implementation is shown as well as computational results on matrix completion problems. In particular, we will consider mildly-ill conditioned and noisy random problems as well as problems arising in diverse applications as the matrix to be recovered represents city-to- city distances, a grayscale image, game parameters in a basketball tournament. This is joint work with S. Bellavia (Unifi) and J. Gondzio (Univ. Edinburgh) https://www.dm.unipi.it/webnew/it/seminari/relaxed-interior-point-methods-l… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar on 14/05 (Alfredo Buttari)
by Leonardo Robol 14 May '21

14 May '21

Speaker: Alfredo Buttari Affiliation: CNRS, IRIT, Toulouse Time: Friday, 14/05/2021, 16:00 Title: Reducing the complexity of linear systems solvers through the block low-rank format Direct linear system solvers are commonly regarded as robust methods for computing the solution of linear systems of equations. Nonetheless, their complexity makes the handling of very large size problems difficult or unfeasible due to excessive execution time or memory consumption. In this talk we discuss the use of low-rank approximation techniques that allow for reducing this complexity at the price of a loss in precision which can be reliably controlled. To take advantage of these low-rank approximations, we have designed a format called block low-rank (BLR) whose objective is to achieve a favorable compromise between complexity and efficiency of operations thanks to its regular structure. We will present the basic BLR format as well as more advanced variants and the associated algorithms; we will analyze their theoretical properties and discuss the issues related to their efficient implementation on parallel computers. We will specifically focus on the use of BLR for the solution of sparse linear systems. The ombination of this format with sparse direct methods, such as the multifrontal one, leads to efficient parallel solvers with scalable complexity. These can either be used as standalone direct solvers or in combination with other techniques such as iterative or multigrid methods. We will present experimental results on real-life problems obtained by integrating the BLR format within the MUMPS parallel sparse direct solver. https://www.dm.unipi.it/webnew/it/seminari/reducing-complexity-linear-syste… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar on 07/05 (Stefano Pozza)
by Leonardo Robol 07 May '21

07 May '21

Speaker: Stefano Pozza Affiliation: Charles University, Prague Time: Friday, 07/05/2021, 16:00 Title: The Short-term Rational Lanczos Method and Applications Rational Krylov subspaces have become a reference tool in dimension reduction procedures for several application problems. When data matrices are symmetric, a short-term recurrence can be used to generate an associated orthonormal basis. In the past this procedure was abandoned because it requires twice the number of linear system solves per iteration than with the classical long-term method. We propose an implementation that allows one to obtain key rational subspace matrices without explicitly storing the whole orthonormal basis, with a moderate computational overhead associated with sparse system solves. Several applications are discussed to illustrate the advantages of the proposed procedure. https://www.dm.unipi.it/webnew/it/seminari/short-term-rational-lanczos-meth… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar on 23/04 (Philipp Birken)
by Leonardo Robol 23 Apr '21

23 Apr '21

Speaker: Philipp Birken Affiliation: Lund University Time: Friday, 23/04/2021, 16:00 Title: Conservative iterative solvers in computational fluid dynamics The governing equations in computational fluid dynamics such as the Navier-Stokes- or Euler equations are conservation laws. Finite volume methods are designed to respect this and the theorem of Lax-Wendroff underscores the importance of it. It roughly states that for a nonlinear (!) scalar conservation law in 1D , if the numerical method with explicit Euler time integration is consistent and (locally) conservative, then in case of convergence, the numerical method converges to a weak solution. When using implicit time integration, the widespread believe in the community is that conservation is lost. This is however, not necessarily due to the time integration, but due to the use of iterative solvers. We first present a catalogue of iterative solvers that preserve the weaker property of global conservation to identify candidates of solvers that preserve local conservation as used in the Lax-Wendroff theorem. We then proceed to prove an extension of the Lax-Wendroff theorem for the situation that we perform a fixed number of steps of a so called pseudo time iteration per time step. It turns out that in this case, the numerical method converges to a weak solution of the conservation law with a modified propagation speed. This can be exploited to improve performance of the iterative method. https://www.dm.unipi.it/webnew/it/seminari/conservative-iterative-solvers-c… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar on 09/04 (Jie Meng)
by Leonardo Robol 09 Apr '21

09 Apr '21

Speaker: Jie Meng Affiliation: Università di Pisa Time: Friday, 09/04/2021, 16:00 Title: Geometric means of quasi-Toeplitz matrices We study means of geometric type of quasi-Toeplitz matrices, that are semi-infinite matrices A = (a_{i,j}) i,j=1,2,... of the form A = T(a) + E, where E represents a compact operator, and T(a) is a semi-infinite Toeplitz matrix associated with the function a, with Fourier series \sum_{l} a_l e^{ilt} , in the sense that (T(a))_{i,j} = a_{j-i}. If a is real valued and essentially bounded, then these matrices represent bounded self-adjoint operators on l^2. We consider the case where a is a continuous function, where quasi-Toeplitz matrices coincide with a classical Toeplitz algebra, and the case where a is in the Wiener algebra, that is, has absolutely convergent Fourier series. We prove that if a_1, ... , a_p are continuous and positive functions, or are in the Wiener algebra with some further conditions, then means of geometric type, such as the ALM, the NBMP and the Karcher mean of quasi-Toeplitz positive definite matrices associated with a_1, ..., a_p , are quasi-Toeplitz matrices associated with the geometric mean (a_1 ... a_p)^{1/p}, which differ only by the compact correction. We show by numerical tests that these operator means can be practically approximated. https://www.dm.unipi.it/webnew/it/seminari/geometric-means-quasi-toeplitz-m… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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[NOMADS] Seminar - Ivan Markovsky - March 30 at 18:00
by Francesco Tudisco 29 Mar '21

29 Mar '21

Dear all, You are all invited to this week's NOMADS seminar at GSSI. The seminar will take place tomorrow *March 30 at 18:00 (CET)*. The speaker is Ivan Markovsky from Vrije Universiteit Brussel (Belgium) who will give a talk on Data-driven dynamic interpolation and approximation. Abstract and more info below. The seminar will be given via Zoom. To attend the seminar please use the following link: https://us02web.zoom.us/j/85393475759?pwd=ckNDOGNGY0d0bTBZVXBmd1FibXJVUT09 <https://us02web.zoom.us/j/85393475759?pwd=ckNDOGNGY0d0bTBZVXBmd1FibXJVUT09> Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Please feel free to distribute this announcement as you see fit. Hope to see you all Tomorrow! Francesco and Nicola ------------------------------------------------- Data-driven dynamic interpolation and approximation The behavioral system theory give theoretical foundation for nonparameteric representations of linear time-invariant systems based on Hankel matrices constructed from data. These data-driven representations led in turn to new system identification, signal processing, and control methods. In particular, data-driven simulation and linear quadratic tracking control problems were solved using the new approach [1,2]. This talk shows how the approach can be used further on for solving data-driven interpolation and approximation problems (missing data estimation) and how it can be generalized to some classes of nonlinear systems. The theory leads to algorithms that are both general (can deal simultaneously with missing, exact, and noisy data of multivariable systems) and simple (require existing numerical linear algebra methods only). This opens a practical computational way of doing system theory and signal processing directly from data without identification of a transfer function or a state space representation and doing model-based design. References: [1] I. Markovsky and P. Rapisarda. “Data-driven simulation and control”. Int. J. Control 81.12 (2008), pp. 1946--1959. [2] I. Markovsky. A missing data approach to data-driven filtering and control. IEEE Trans. Automat. Contr., 62:1972--1978, April 2017. [3] I. Markovsky and F. Dörfler. Data-driven dynamic interpolation and approximation. Technical report, Vrije Universiteit Brussel, 2021. Available from http://homepages.vub.ac.be/~imarkovs/publications/ddint.pdf — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io <https://ftudisco.gitlab.io> -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/51aafd85-e7f6-58a0-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Seminar on 19/03 (Alice Cortinovis)
by Leonardo Robol 19 Mar '21

19 Mar '21

Speaker: Alice Cortinovis Affiliation: EPFL Time: Friday, 19/03/2021, 16:00 Title: Randomized trace estimates for indefinite matrices with an application to determinants Randomized trace estimation is a popular technique to approximate the trace of a large-scale matrix A by computing the average of quadratic forms x^T * A * x for many samples of a random vector X. We show new tail bounds for randomized trace estimates in the case of Rademacher and Gaussian random vectors, which significantly improve existing results for indefinite matrices. Then we focus on the approximation of the determinant of a symmetric positive definite matrix B, which can be done via the relation log(det(B)) = trace(log(B)), where the matrix log(B) is usually indefinite. We analyze the convergence of the Lanczos method to approximate quadratic forms x^T * log(B) * x by exploiting its connection to Gauss quadrature. Finally, we combine our tail bounds on randomized trace estimates with the analysis of the Lanczos method to improve and extend an existing result on log determinant approximation to not only cover Rademacher but also Gaussian random vectors. https://www.dm.unipi.it/webnew/it/seminari/randomized-trace-estimates-indef… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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[NOMADS] Seminar - Eugene Tyrtyshnikov - Today at 18:00
by Francesco Tudisco 09 Mar '21

09 Mar '21

Good morning everyone, This is just a gentle reminder about *today's seminar by Eugene Tyrtyshnikov* (MSU and INM-RAS). The seminar will take place *at 18:00* via the Zoom meeting: https://us02web.zoom.us/j/84101660726?pwd=TDhrWlFKdnhQVnBTZFdMWmw3Q3J4QT09 Hope to see you all there! Francesco and Nicola ---------------- Tikhonov's solution to a class of linear systems equivalent within perturbations A standard approach to incorrect problems suggests that a problem of interest is reformulated with the knowledge of some additional a-priori information. This can be done by several well-known regularization techniques. Many practical problems are successfully solved on this way. What does not still look as completely satisfactory is that the new reset problem seems to appear rather implicitly in the very process of its solution. In 1980, A. N. Tikhonov proposed a reformulation [1] that arises explicitly before the discussion of the solution methods. He suggested a notion of normal solution to a family of linear algebraic systems described by a given individual system and its vicinity comprising perturbed systems, under the assumption that there are compatible systems in the class notwithstanding the compatibility property of the given individual system. Tikhovov proved that the normal solution exists and is unique. However, a natural question about the correctness of the reset problem was not answered. In this talk we address a question of correctness of the reformulated incorrect problems that seems to have been missed in all previous considerations. The main result is the proof of correctness for Tikhonov's normal solution. Possible generalizations and difficulties will be also discussed. [1] A. N. Tikhonov, Approximate systems of linear algebraic equations, USSR Computational Mathematics and Mathematical Physics, vol. 20, issue 6 (1980) — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/2fe6fc1f-c30c-9ee8-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar - Eugene Tyrtyshnikov - March 9 at 18:00
by Francesco Tudisco 08 Mar '21

08 Mar '21

Dear all, You are all invited to this week's NOMADS seminar at GSSI. *The seminar schedule is changed and will now run on Tuesdays @ 18:00 (CET)* most of the times. This week's seminar is on *March 09 at 18:00 (CET).* The speaker is Eugene Tyrtyshnikov from Moscow University and INM-RAS (Russia). The talk will be focused on the Tikhonov solution to a class of linear system problems. Please find abstract and title below. The seminar will be given via Zoom. To attend the seminar please use the following link: https://us02web.zoom.us/j/84101660726?pwd=TDhrWlFKdnhQVnBTZFdMWmw3Q3J4QT09 Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Please feel free to distribute this announcement as you see fit. Hope to see you all on Tuesday! Francesco and Nicola ------ Tikhonov's solution to a class of linear systems equivalent within perturbations A standard approach to incorrect problems suggests that a problem of interest is reformulated with the knowledge of some additional a-priori information. This can be done by several well-known regularization techniques. Many practical problems are successfully solved on this way. What does not still look as completely satisfactory is that the new reset problem seems to appear rather implicitly in the very process of its solution. In 1980, A. N. Tikhonov proposed a reformulation [1] that arises explicitly before the discussion of the solution methods. He suggested a notion of normal solution to a family of linear algebraic systems described by a given individual system and its vicinity comprising perturbed systems, under the assumption that there are compatible systems in the class notwithstanding the compatibility property of the given individual system. Tikhovov proved that the normal solution exists and is unique. However, a natural question about the correctness of the reset problem was not answered. In this talk we address a question of correctness of the reformulated incorrect problems that seems to have been missed in all previous considerations. The main result is the proof of correctness for Tikhonov's normal solution. Possible generalizations and difficulties will be also discussed. [1] A. N. Tikhonov, Approximate systems of linear algebraic equations, USSR Computational Mathematics and Mathematical Physics, vol. 20, issue 6 (1980) — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/CAO2_FWkAyR1tebRPom…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Seminar on 05/03 (Davide Bianchi)
by Leonardo Robol 05 Mar '21

05 Mar '21

Speaker: Davide Bianchi Affiliation: University of Insubria Time: Friday, 05/03/2021, 16:00 Title: Compatibility, embedding and regularization of non-local random walks on graphs Several variants of the graph Laplacian have been introduced to model non-local diffusion pro- cesses, which allow a random walker to “jump” to non-neighborhood nodes, most notably the path graph Laplacians and the fractional graph Laplacian, see [2, 3]. From a rigorous point of view, this new dynamics is made possible by having replaced the original graph G with a weighted complete graph G 0 on the same node-set, that depends on G and wherein the presence of new edges allows a direct passage between nodes that were not neighbors in G. A natural question arises: are the dynamics on the “old” walks along the edges of G compatible with the new dynamics? Indeed, it would be desirable to introduce long-range jumps but preserving at the same time the original dynamics if we move along the edges of G. In other words, for any time-interval where does not take place any long-range jump, a random walk on G 0 should be indistinguishable from the original random walk on G. One can easily figure this by a simple but clarifying example: let us suppose that our random walker is surfing the Net (the original graph G), and just for the sake of simplicity let us suppose that the Net is undirected. The walker then can move towards linked web-pages with a probability that can be both uniforms on the number of total links or dependent on some other parameters. Suppose now that we allow the walker to jump from one web-page to non-linked web-pages by just typing an URL address in the navigation bar so that he can virtually reach directly any possible web-pages on the Net (the induced graph G 0 ). If in any moment, for any reason, the walker is forced again to surf the Net by just following the links, then we should see him moving exactly as he used to do, namely, the probability he moves to the next linked web-page has to be the same as before. Unfortunately, in general, the induced complete graph G 0 , defined accordingly to the proposal in the literature, breaks that compatibility and the new models cease to be expressions of the original model G. In this talk, we will present some of the main results obtained in [1]. We will first introduce a rigorous definition of compatibility and embedding, which stem from a probabilistic and purely an- alytical point of view, respectively. Secondly, we will propose a regularization method to guarantee such compatibility and preserving at the same time all the nice properties granted by G 0 . Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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[NOMADS] Seminar - Michael Schaub - Today at 18:00
by Francesco Tudisco 17 Feb '21

17 Feb '21

Good morning everyone, This is just a gentle reminder about *today's seminar* on "Learning from signals on graphs with unobserved edges" by Michael Schaub (RWTH Aachen University). Abstract below. Please note that the seminar talk has been pushed back by one hour and *will take place at 18:00*. The Zoom link for the talk is: https://us02web.zoom.us/j/87171939595 Hope to see you all there! Francesco and Nicola ---------------------------------------------- Speaker: Michael Schaub, RWTH Aachen University https://michaelschaub.github.io/ Title: Learning from signals on graphs with unobserved edges Abstract: In many applications we are confronted with the following system identification scenario: we observe a dynamical process that describes the state of a system at particular times. Based on these observations we want to infer the (dynamical) interactions between the entities we observe. In the context of a distributed system, this typically corresponds to a "network identification" task: find the (weighted) edges of the graph of interconnections. However, often the number of samples we can obtain from such a process are far too few to identify the edges of the network exactly. Can we still reliably infer some aspects of the underlying system? Motivated by this question we consider the following identification problem: instead of trying to infer the exact network, we aim to recover a (low-dimensional) statistical model of the network based on the observed signals on the nodes. More concretely, here we focus on observations that consist of snapshots of a diffusive process that evolves over the unknown network. We model the (unobserved) network as generated from an independent draw from a latent stochastic blockmodel (SBM), and our goal is to infer both the partition of the nodes into blocks, as well as the parameters of this SBM. We present simple spectral algorithms that provably solve the partition and parameter inference problems with high-accuracy. We further discuss some possible variations and extensions of this problem setup. This talk is part of NOMADS — Numerical ODEs, Matrix Analysis and Data Science — seminar at GSSI: https://num-gssi.github.io/seminar/ — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/c82561f8-8a98-5698-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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NumPi seminars - Doodle
by Leonardo Robol 15 Feb '21

15 Feb '21

Dear all, as usual, we will soon start with the NumPi seminars for the second semester. As in the first semester, they will be online. In order to minimize the overlap with teaching activities and other commitments, we have prepared a Doodle where (if you wish to attend the seminars) you can choose your preferred time slot(s). Please note that the Doodle is for this week, but it is intended for a "generic week" of this semester. The first seminar will likely be at the beginning of March. Doodle link: https://doodle.com/poll/a4fpmfwat7q62rnu P.S.: In case you wish to propose some speakers (or yourself as a speaker), feel free to drop us an e-mail. Best wishes, -- Fabio Durastante and Leonardo Robol.

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[NOMADS] Seminar - Michael Schaub - Feb 17 at 17:00
by Francesco Tudisco 15 Feb '21

15 Feb '21

Dear all, You are all invited to this week's NOMADS seminar at GSSI. The seminar will be on Wednesday February 17 at 17:00 (CET) by Michael Schaub from RWTH Aachen University (Germany). The talk will be focused on a method for learning the structure of a network given few observations of a diffusive process on the unknown graph. Title and abstract are below. To attend the semimar please use the following link: https://us02web.zoom.us/j/87171939595 Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Hope to see you all on Wednesday! And, please feel free to distribute this announcement as you see fit. Francesco and Nicola -------- Title: Learning from signals on graphs with unobserved edges In many applications we are confronted with the following system identification scenario: we observe a dynamical process that describes the state of a system at particular times. Based on these observations we want to infer the (dynamical) interactions between the entities we observe. In the context of a distributed system, this typically corresponds to a "network identification" task: find the (weighted) edges of the graph of interconnections. However, often the number of samples we can obtain from such a process are far too few to identify the edges of the network exactly. Can we still reliably infer some aspects of the underlying system? Motivated by this question we consider the following identification problem: instead of trying to infer the exact network, we aim to recover a (low-dimensional) statistical model of the network based on the observed signals on the nodes. More concretely, here we focus on observations that consist of snapshots of a diffusive process that evolves over the unknown network. We model the (unobserved) network as generated from an independent draw from a latent stochastic blockmodel (SBM), and our goal is to infer both the partition of the nodes into blocks, as well as the parameters of this SBM. We present simple spectral algorithms that provably solve the partition and parameter inference problems with high-accuracy. We further discuss some possible variations and extensions of this problem setup. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/2f2274b3-9a34-5b45-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar - Lothar Reichel - Today at 17:00
by Francesco Tudisco 04 Feb '21

04 Feb '21

Good morning everyone, This is just a gentle reminder about today's seminar "Large-scale regression with non-convex loss and penalty" by Lothar Reichel (Kent State University, USA). Abstract below. The seminar is at 17:00 (CET). To attend please use the zoom link: https://us02web.zoom.us/j/89724684523 Please feel free to distribute this announcement as you see fit. Hope to see you there! Francesco and Nicola ---------- Title: Large-scale regression with non-convex loss and penalty Description: We do non-convex optimization with application to image restoration and regression problems for which a sparse solution is desired. ---------- — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/02613376-994d-c51e-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar - Lothar Reichel - Feb 4 at 17:00
by Francesco Tudisco 01 Feb '21

01 Feb '21

Dear all, You are all invited to this week's NOMADS seminar at GSSI. The seminar will be given on *Thursday* (not Wednesday as usual) *February 4 at 17:00 (CET)* by *Lothar Reichel* from Kent State University (USA). --- Title: Large-scale regression with non-convex loss and penalty Description: We do non-convex optimization with application to image restoration and regression problems for which a sparse solution is desired. --- To attend the seminar please use the following link: https://us02web.zoom.us/j/89724684523 Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Please feel free to distribute this announcement as you see fit. Hope to see you all on Thursday! Francesco and Nicola — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/2f5d2866-9537-1186-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Fwd: Summer School plus Conference on “Mathematics for Nonstationary Signals,and applications in Geophysics and other fields” - L'Aquila (Italy) and online, July 2021
by Federico Poloni 30 Jan '21

30 Jan '21

Inoltro questo annuncio per i potenziali interessati non iscritti al GNCS. Buon week-end, -federico -------- Forwarded Message -------- Subject: Summer School plus Conference on “Mathematics for Nonstationary Signals,and applications in Geophysics and other fields” - L'Aquila (Italy) and online, July 2021 Date: Sat, 30 Jan 2021 10:29:15 +0100 From: Ruggiero Valeria <valeria.ruggiero(a)unife.it> To: gncs-aderenti(a)altamatematica.it Dear Colleagues, we kindly inform you that a Summer School plus Conference on “Mathematics for Nonstationary Signals and applications in Geophysics and other fields”, will take place at the Università degli Studi dell'Aquila, L'Aquila, Italy, and online on July 19-24, 2021. The event will be hybrid, providing the opportunity to everyone to join either in-person or virtually. During the Summer School young researchers and PhD students will have a chance to learn and deepen their knowledge on Mathematics of Signal Processing, in particular on new data analysis tools/techniques for non-stationary time series and their theoretical foundation. The summer school will take place during the first 4 days and it will consist of three courses of 8 hours each. Confirmed Lecturers: Patrick Flandrin - ENS Lyon Yang Wang - HKSTU Hau-tieng Wu - Duke University At the end of the school there will be a 2 days and half Conference and Poster Session during which the speakers will show both the applications of these techniques to real life data and present the current frontiers of the theoretical research. Some slots for contributed talks and posters are still available. Contributed talks will be 30 minutes long (25+5 for questions). Submission deadline is April 30, 2021. Applications for prospective students of the Summer School, as well as speakers of the conference and poster session are now open. Financial support is available for a limited number of participants. For more information and to apply please visit www.cicone.com/NoSAG21.html <http://www.cicone.com/NoSAG21.html> Best regards, The local organizing committee Antonio Cicone - DISIM - Università degli Studi dell'Aquila - L'Aquila Giulia D'Angelo - INAF - Istituto di Astrofisica e Planetologia Spaziali - Roma Enza Pellegrino - DIIIE - Università degli Studi dell'Aquila - L'Aquila Mirko Piersanti - INFN - Universita di Roma "Tor Vergata" - Roma Angela Stallone - INGV - Istituto Nazionale di Geofisica e Vulcanologia - Roma

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Math Colloquium - Anders Hansen - Jan 28
by Francesco Tudisco 28 Jan '21

28 Jan '21

Dear all, * *the next GSSI Math Colloquium will be held on *Thursday January 28 *at***3pm* (Italian time). The speaker is Anders Hansen, <http://www.damtp.cam.ac.uk/research/afha/anders/> with a lecture connecting computational mathematics with deep learning and AI. More details below. Anders Hansen is Associate Professor at University of Cambridge, where he leads the Applied Functional and Harmonic Analysis group, and Full Professor of Mathematics at the University of Oslo. To attend the talk please use to the following *Zoom link*: https://us02web.zoom.us/j/84038062394 Please feel free to distribute this announcement as you see fit. Looking forward to seeing you all on Thursday! Paolo Antonelli, Stefano Marchesani, Francesco Tudisco and Francesco Viola --------------------- Title: On the foundations of computational mathematics, Smale's 18th problem and the potential limits of AI Abstract: There is a profound optimism on the impact of deep learning (DL) and AI in the sciences with Geoffrey Hinton concluding that 'They should stop training radiologists now'. However, DL has an Achilles heel: it is universally unstable so that small changes in the initial data can lead to large errors in the final result. This has been documented in a wide variety of applications. Paradoxically, the existence of stable neural networks for these applications is guaranteed by the celebrated Universal Approximation Theorem, however, the stable neural networks are never computed by the current training approaches. We will address this problem and the potential limitations of AI from a foundations point of view. Indeed, the current situation in AI is comparable to the situation in mathematics in the early 20th century, when David Hilbert’s optimism (typically reflected in his 10th problem) suggested no limitations to what mathematics could prove and no restrictions on what computers could compute. Hilbert’s optimism was turned upside down by Goedel and Turing, who established limitations on what mathematics can prove and which problems computers can solve (however, without limiting the impact of mathematics and computer science). We predict a similar outcome for modern AI and DL, where the limitations of AI (the main topic of Smale’s 18th problem) will be established through the foundations of computational mathematics. We sketch the beginning of such a program by demonstrating how there exist neural networks approximating classical mappings in scientific computing, however, no algorithm (even randomised) can compute such a network to even 1-digit accuracy (with probability better than 1/2). We will also show how instability is inherit in the methodology of DL demonstrating that there is no easy remedy, given the current methodology. Finally, we will demonstrate basic examples in inverse problems where there exists (untrained) neural networks that can easily compute a solution to the problem, however, the current DL techniques will need 10^80 data points in the training set to get even 1% success rate. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/b3099d6a-bcef-2052-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Postdoc Position, Krylov Methods, Charles Univ, Czech Rep
by Federico Poloni 25 Jan '21

25 Jan '21

Buongiorno, inoltro questo annuncio, che può essere di interesse per qualche iscritto alla lista. **Postdoc Position, Krylov Methods, Charles Univ, Czech Rep** A postdoc position is available within the framework of the Primus Research Programme "A Lanczos-like Method for the Time-Ordered Exponential" at the Faculty of Mathematics and Physics, Charles University, Prague. The appointment period is one year, with the possibility of extension. The postdoc will start before the end of 2021. The start date is negotiable. We are looking for candidates with a strong background in numerical linear algebra. In particular, we seek applicants with expertise in matrix function approximation and Krylov subspace methods. The applicant must hold a Ph.D. degree by the start date. Application deadline: March 15, 2021. More information and application instructions: https://www.starlanczos.cz/open-positions <https://www.starlanczos.cz/open-positions> -- --federico poloni Dipartimento di Informatica, Università di Pisa https://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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NEPA Seminar (D. Bini)
by Leonardo Robol 15 Jan '21

15 Jan '21

Dear all, on January 19, 3 pm, Dario Bini will give a talk on "Solving Structured Matrix Equations Encountered in the Analysis of Stochastic Processes". The talk is part of the NEPA seminar series, and many more talks will take place in the next weeks. Participation is free, but a registration is required to obtain the Zoom link [1]. [1] https://sites.google.com/unisa.it/nepaseminars Best wishes, -- Leonardo.

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[NOMADS] Seminar - Gianluca Ceruti - Today at 17:00
by Francesco Tudisco 13 Jan '21

13 Jan '21

Good morning everyone, This is just a gentle reminder about today's seminar "Numerical integrators for dynamical low-rank approximation" by Gianluca Ceruti (Uni Tuebingen). Abstract below. The seminar is at 17:00 (CET). To attend please use the zoom link: https://us02web.zoom.us/j/82131676880 Hope to see you there! Francesco and Nicola ----------- Gianluca Ceruti <https://na.uni-tuebingen.de/~ceruti/> - University of Tuebingen Numerical integrators for dynamical low-rank approximation Discretization of time-dependent high-dimensional PDEs suffers of an undesired effect, known as curse of dimensionality. The amount of data to be stored and treated, grows exponentially, and exceeds standard capacity of common computational devices. In this setting, time dependent model order reductions techniques are desirable. In the present seminar, together with efficient numerical integrators, we present a recently developed approach: dynamical low-rank approximation. Dynamical low-rank approximation for matrices will be firstly presented, and a numerical integrator with two remarkable properties will be introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we will construct two equivalent extensions for tensors, multi-dimensional arrays, in Tucker format - a high-order generalization of the SVD decomposition for matrices. These extensions are proven to preserve the excellent qualities of the matrix integrator. To conclude, via a novel compact formulation of the Tucker integrator, we will further extend the matrix and Tucker projector splitting integrators to the most general class of Tree Tensor Networks. Important examples belonging to this class and of interest for applications are given, but not only restricted to, by Tensor Trains. This seminar is based upon a joint work with Ch. Lubich and H. Walach. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/46a4a726-fee9-9f0b-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar - Gianluca Ceruti - Jan 13 at 17:00
by Francesco Tudisco 11 Jan '21

11 Jan '21

Dear all, We hope you all had joyful holidays and wish you all a great start for the new year! We are ready to start with this year's NOMADS seminar at GSSI and would like to invite you to this week's talk. The seminar will be given on Wednesday January 13 at 17:00 (CET) by Gianluca Ceruti from University of Tuebingen. Title, abstract and zoom link are below. Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Please feel free to distribute this announcement as you see fit. Hope to see you all on Wednesday! Francesco and Nicola ================================ Speaker: Gianluca Ceruti, University of Tuebingen https://na.uni-tuebingen.de/~ceruti/ Zoom link: https://us02web.zoom.us/j/82131676880 Numerical integrators for dynamical low-rank approximation Discretization of time-dependent high-dimensional PDEs suffers of an undesired effect, known as curse of dimensionality. The amount of data to be stored and treated, grows exponentially, and exceeds standard capacity of common computational devices. In this setting, time dependent model order reductions techniques are desirable. In the present seminar, together with efficient numerical integrators, we present a recently developed approach: dynamical low-rank approximation. Dynamical low-rank approximation for matrices will be firstly presented, and a numerical integrator with two remarkable properties will be introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we will construct two equivalent extensions for tensors, multi-dimensional arrays, in Tucker format - a high-order generalization of the SVD decomposition for matrices. These extensions are proven to preserve the excellent qualities of the matrix integrator. To conclude, via a novel compact formulation of the Tucker integrator, we will further extend the matrix and Tucker projector splitting integrators to the most general class of Tree Tensor Networks. Important examples belonging to this class and of interest for applications are given, but not only restricted to, by Tensor Trains. This seminar is based upon a joint work with Ch. Lubich and H. Walach. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/CAO2_FW%3DqD1z%3D9V…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar - Alexander Viguerie - Dec 16 at 17:00
by Francesco Tudisco 16 Dec '20

16 Dec '20

Dear all, You are all invited to this week's NOMADS seminar at GSSI. The seminar will be given on *Wednesday December 16 at 17:00* (CET) by *Alexander Viguerie* from GSSI. Title, abstract and zoom link are below. This is the last seminar of 2020 and we will then be back on Jan 13, 2021. Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Please feel free to distribute this announcement as you see fit. Hope to see you all on Wednesday! Francesco and Nicola ================================================== Zoom link: https://us02web.zoom.us/j/89492628943 Speaker: Alexander Viguerie <https://www.gssi.it/people/post-doc/post-doc-maths/item/11289-viguerie-alex> Title: Efficient, stable, and reliable solvers for the Steady Incompressible Navier-Stokes equations: application to Computational Hemodynamics. Abstract: Over the past several years, computational fluid dynamics (CFD) simulations have become increasingly popular as a clinical tool for cardiologists at the patient-specific level. The use of CFD in this area poses several challenges. The clinical setting places heavy restrictions on both computational time and power. Simulation results are usually desired within minutes and are usually run on standard computers. For these reasons, steady-state Navier-Stokes simulations are usually preferred, as they can be completed in a fraction of the time required to run an unsteady computation. However, in many respects the steady problem is more difficult than the unsteady one, particularly in regards to solving the associated linear and nonlinear systems. Additionally, boundary data for patient-specific problems is often missing, incomplete, or unreliable. This makes the determination of a useful model challenging, as it requires the generation of reliable boundary data without introducing heavy computational costs. This seminar will address these challenges, as well as some others, and introduce new techniques for workarounds. Results from patient-specific cases will be presented and discussed. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/54b94f9a-5840-e31c-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Seminario di Des Higham
by Dario A. Bini 04 Dec '20

04 Dec '20

Buongiorno, vi informo che oggi alle 15:00 Desmond Higham (University of Edinburgh), presenterà un seminario dal titolo "/A Hierarchy of //Network Models Giving Bistability Under Triadic Closure/". L'abstract e' allegato. Per registrarsi e ricevere il link per partecipare via Zoom cliccare su https://sites.google.com/unisa.it/nepaseminars A presto, Dario --- Abstract: Triadic closure describes the tendency for new friendships to form between individuals who already have friends in common. It has been argued heuristically that the triadic closure effect can lead to bistability in the formation of large-scale social interaction networks. Here, depending on the initial state and the transient dynamics, the system may evolve towards either of two long-time states. In this work, we study a hierarchy of network evolution models that incorporate triadic closure, building on the work of Grindrod, Higham and Parsons [Internet Mathematics, 8, 2012, 402--423]. In a macroscale regime, we show rigorously that a bimodal steady state distribution is admitted. Computational simulations will be used to support the analysis. This is joint work work with Stefano Di Giovacchino (L'Aquila) and Kostas Zygalakis (Edinburgh).

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[NOMADS] Seminar - Martin Stoll - Today at 17:00
by Francesco Tudisco 02 Dec '20

02 Dec '20

Good morning everyone, This is just a gentle reminder about today's seminar "From PDEs to data science: an adventure with the graph Laplacian" by Martin Stoll (TU-Chemnitz). Abstract below. The seminar is at 17:00 (CET). To attend, please use the zoom link: https://us02web.zoom.us/j/81317396646 Hope to see you there! Francesco and Nicola ------ Martin Stoll <https://www.tu-chemnitz.de/mathematik/wire/prof.php>, TU-Chemnitz From PDEs to data science: an adventure with the graph Laplacian In this talk we briefly review some basic PDE models that are used to model phase separation in materials science. They have since become important tools in image processing and over the last years semi-supervised learning strategies could be implemented with these PDEs at the core. The main ingredient is the graph Laplacian that stems from a graph representation of the data. This matrix is large and typically dense. We illustrate some of its crucial features and show how to efficiently work with the graph Laplacian. In particular, we need some of its eigenvectors and for this the Lanczos process needs to be implemented efficiently. Here, we suggest the use of the NFFT method for evaluating the matrix vector products without even fully constructing the matrix. We illustrate the performance on several examples. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/002e39cd-038e-e9cc-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Seminar on 01/12 (Fabio Durastante)
by Leonardo Robol 01 Dec '20

01 Dec '20

Speaker: Fabio Durastante Affiliation: IAC-CNR (...that will soon become University of Pisa) Time: Tuesday, 01/12/2020, 16:00 Title: (Sparse) Linear Algebra at the Extreme Scales Sparse linear algebra is essential for a wide variety of scientific applications. The availability of highly parallel sparse solvers and preconditioners lies at the core of pretty much all multi-physics and multi-scale simulations. Technology is nowadays expanding to target exascale platforms. I am going to present some work on Algebraic Multigrid Preconditioners in which we try to face these challenges to make Exascale Computing possible. The talk will focus on one side on the theoretical aspects pertaining to the construction of the multigrid hierarchy for which the main novelty is the design and implementation of new parallel smoothers and a coarsening algorithm based on aggregation of unknowns employing weighted graph matching techniques. On the other, the talk also focuses on the libraries developed to cover the needs of having parallel BLAS feature for sparse matrices that are capable of running on machines with thousands of high-performance cores; and to discuss the advancements made by the new smoothers and coarsening algorithm as an improvement in terms of numerical scalability at low operator complexity over the algorithms available in previous releases of the package. I will present weak scalability results on two of the most powerful supercomputers in Europe, for linear systems with sizes up to O(10^10) unknowns for a benchmark Poisson problem, and strong scaling result for a wind-simulation benchmark problem. This is a joint work with P. D’Ambra, and S. Filippone. This work is supported by the EU under the Horizon 2020 Project Energy oriented Centre of Excellence: toward exascale for energy (EoCoE-II), Project ID: 824158 Meeting link: <https://hausdorff.dm.unipi.it/b/leo-xik-xu4>

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NOMADS seminar @GSSI - Wed 2 - Martin Stoll
by Francesco Tudisco 30 Nov '20

30 Nov '20

Dear all, You are all invited to this week's NOMADS seminar at GSSI. The seminar will be given by Martin Stoll from TU-Chemnitz (Germany). Title, abstract and zoom link are below. Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Please feel free to distribute this announcement as you see fit. Hope to see you all on Wednesday! Francesco and Nicola ================================================== Title: From PDEs to data science: an adventure with the graph Laplacian Abstract: In this talk we briefly review some basic PDE models that are used to model phase separation in materials science. They have since become important tools in image processing and over the last years semi-supervised learning strategies could be implemented with these PDEs at the core. The main ingredient is the graph Laplacian that stems from a graph representation of the data. This matrix is large and typically dense. We illustrate some of its crucial features and show how to efficiently work with the graph Laplacian. In particular, we need some of its eigenvectors and for this the Lanczos process needs to be implemented efficiently. Here, we suggest the use of the NFFT method for evaluating the matrix vector products without even fully constructing the matrix. We illustrate the performance on several examples. Zoom: https://us02web.zoom.us/j/81317396646 — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/c28372f5-7312-f490-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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You have been added to nomads-list
by nomads-list 30 Nov '20

30 Nov '20

Hi numpi(a)di.unipi.it, francesco.tudisco(a)gssi.it added you to the group nomads-list. https://groups.google.com/a/gssi.it/d/forum/nomads-list About this group: Mailing list for nomads seminar @gssi Google Groups allows you to create and participate in online forums and email-based groups with a rich community experience. You can also use your Group to share documents, pictures, calendars, invitations and other resources. If you do not wish to be a member of this group or believe that this group may contain spam: * You can unsubscribe from this group at https://groups.google.com/a/gssi.it/d/forum/nomads-list/unsubscribe/AHZ7KVN… or by sending an email to nomads-list+unsubscribe(a)gssi.it * You can report this group for abuse at https://groups.google.com/a/gssi.it/d/abuse/AJmrmCv0R3hRW4gfW4hkqLtrztlR3zN… * You can opt out of all future Google Groups activity at https://groups.google.com/a/gssi.it/d/optout Visit the Google Groups Help Centre at https://support.google.com/groups/answer/46601?hl=en_GB.

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Scomparsa Prof. Alfonso Laratta
by Paolo ghelardoni 27 Nov '20

27 Nov '20

Cari tutti, ho appena ricevuto da Luca Zanni la mail che segue. Io non sono piu' iscritto al GNCS. Se qualcuno di voi vuole prendere accordi con Luca per fare la comunicazione al GNCS, nella mail e' riportato anche il suo numero di cellulare. Ciao Paolo -------- Messaggio Inoltrato -------- Oggetto: scomparsa Prof. Alfonso Laratta Data: Fri, 27 Nov 2020 08:30:56 +0100 Mittente: Luca ZANNI <luca.zanni(a)unimore.it> Organizzazione: Università di Modena e Reggio Emilia A: menchi(a)di.unipi.it, paolo.ghelardoni(a)unipi.it Cari Ornella e Paolo, mi rivolgo a voi perchè sono certo che avevate avuto collaborazioni con Alfonso. Ieri pomeriggio ho saputo della sua scomparsa e sicuramente ne sarete a conoscenza anche voi. Ho fatto un avviso per il mio dipartimento e pensavo di fare una comunicazione anche al GNCS, magari insieme a qualche collega di Pisa, visto che l'attività di Alfonso si divise tra le due sedi. Cosa ne dite? Vi lascio il mio cellulare nel caso servisse sentirsi: 331 6074422 Un caro saluto L. -- ********************************************************************* * Prof. Luca Zanni * office: +39 059 2055206 * * Dipartimento di Scienze Fisiche, Informatiche e Matematiche * * Universita' di Modena e Reggio Emilia * fax: +39 059 2055216 * * Via Campi, 213/b * * 41125 - Modena - ITALY * e-mail: luca.zanni(a)unimore.it * ********************************************************************* -- Paolo Ghelardoni Dipartimento di Matematica Sede -- Via Buonarroti 1/C 56127 Pisa (Italia) Tel: +39 050 2213867 E-mail: paolo.ghelardoni(a)unipi.it Home Page: http://pagine.dm.unipi.it/ghelardoni

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Next NumPi Seminar (Doodle)
by Leonardo Robol 25 Nov '20

25 Nov '20

Dear all, next week Fabio Durastante, which will soon officially join the Department of Mathematics, will give a talk in the NumPi series. Some of you recently told me that the usual time slot (Tue 11:00 -- 12:00) does not work well anymore, due to new teaching obligations. Hence, I am preparing a new Doodle to evaluate changing the day and time of the seminar for this (and possibly the next) seminar; I am kindly asking if you could fill in the Doodle by Friday, so I can then make a decision and send the announcement. Here is the link for the Doodle: https://doodle.com/poll/5uq983z7s686qdp6 Thanks! Best wishes, -- Leonardo Robol.

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Seminar on 17/11 (Francesco Tudisco)
by Leonardo Robol 17 Nov '20

17 Nov '20

Speaker: Francesco Tudisco Affiliation: GSSI Time: Tuesday, 17/11/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: A tensor method for semi-supervised learning Semi-supervised learning is the problem of finding clusters in a graph or a point-clould dataset where we are given "few" initial input labels. Label Spreading (LS) is a standard technique for this problem, which can be interpreted as a diffusion process of the labels on the graph. While there are many variants of LS, nearly all of them are linear models which, for every node, only account for the information incoming from its direct neighbors. Recent work in network science has shown that in many graph algorithms a great advantage can be obtained when accounting directly for higher-order features. Such features may be built from the point-cloud data or the adjacency matrix, for example by considering a triangle involving nodes i, j and k. In other contexts, higher-order information appears explicitly, for example, in a coauthorship network, a document with three authors forms a natural triangle. After reviewing the original LS algorithm I will present our proposed variation of it, which takes directly advantage of higher-order information. A key point of the proposed method is that we replace the standard Laplacian matrix with a nonlinear Laplacian-inspired map which is defined in terms of a order-three tensor. Just like standard LS, we can show convergence of the new nonlinear diffusion process to the gloabal minimum of a constrained semi-supervised loss function that enforces local and global consistency with the input labels. We demonstrate the efficiency and efficacy of our approach on a variety of point cloud and network datasets, where the proposed model outperforms classical label spreading, hypergraph clustering methods, and graph neural networks. I will also point out some open problems related to both the modeling part and the computational one. https://www.dm.unipi.it/webnew/it/seminari/tensor-method-semi-supervised-le…

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NOMADS seminar @GSSI - Nov 18 and Nov 20
by Francesco Tudisco 16 Nov '20

16 Nov '20

Dear all, We are happy to invite you all to the next NOMADS (Numerical ODEs, Matrix Analysis and Data Science) seminar at GSSI. This week we will have two talks, as per the following schedule: 1) Christian Lubich, University of Tuebingen, Germany Wednesday November 18, 17h00 (CET) 2) Patricia Diaz De Alba, Gran Sasso Science Institute, Italy Friday November 20, 17h15 (CET) All seminars take place via Zoom. See below for additional information (e.g. title, abstract and zoom link). Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Please feel free to distribute this announcement as you see fit. Hope to see you all on Wednesday and Friday! Francesco Tudisco and Nicola Guglielmi --------------------------------------------------------------------- November 18, 2020 (Wednesday) at 17h00 (Italian time) Christian Lubich <https://na.uni-tuebingen.de/~lubich/> *Dynamical low-rank approximation* This talk reviews differential equations and their numerical solution on manifolds of low-rank matrices or of tensors with a rank structure such as tensor trains or general tree tensor networks. These low-rank differential equations serve to approximate, in a data-compressed format, large time-dependent matrices and tensors or multivariate functions that are either given explicitly via their increments or are unknown solutions to high-dimensional evolutionary differential equations, with multi-particle time-dependent Schrödinger equations and kinetic equations such as Vlasov equations as noteworthy examples of applications. Recently developed numerical time integrators are based on splitting the projection onto the tangent space of the low-rank manifold at the current approximation. In contrast to all standard integrators, these projector-splitting methods are robust to the unavoidable presence of small singular values in the low-rank approximation. This robustness relies on exploiting geometric properties of the manifold of low-rank matrices or tensors: in each substep of the projector-splitting algorithm, the approximation moves along a flat subspace of the low-rank manifold. In this way, high curvature due to small singular values does no harm. This talk is based on work done intermittently over the last decade with Othmar Koch, Bart Vandereycken, Ivan Oseledets, Emil Kieri, Hanna Walach and Gianluca Ceruti. Zoom link <https://us02web.zoom.us/j/83782294125> Add event to Google calendar <https://calendar.google.com/event?action=TEMPLATE&tmeid=MW83YTByZm1ia2E0MGp…> ------------------------------------------------------------------- ------------------------------------------------------------------- November 20, 2020 (Friday) at 17h30 (Italian time) Patricia Diaz De Alba <http://bugs.unica.it/~patricia/> *Numerical treatment for inverse electromagnetic problems* Electromagnetic induction surveys are among the most popular techniques for non-destructive investigation of soil properties, in order to detect the presence of both ground inhomogeneities and particular substances. Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Based on a non-linear forward model used to describe the interaction between an electromagnetic field and the soil, the aim is to reconstruct the distribution of either the electrical conductivity or the magnetic permeability with respect to depth. To this end, the inversion of both the real (in-phase) and the imaginary (quadrature) components of the signal are studied by a regularized damped Gauss-Newton method. The regularization part of the algorithm is based on a low-rank approximation of the Jacobian of the non-linear model. Furthermore, in many situations, a regularization scheme retrieving smooth solutions is blindly applied, without taking into account the prior available knowledge. An algorithm for a regularization method that promotes the sparsity of the reconstructed electrical conductivity or magnetic permeability distribution is available. This regularization strategy incorporates a minimum gradient support stabilizer into a truncated generalized singular value decomposition scheme. The whole inversion algorithm has been enclosed in a MATLAB package, called FDEMtools, allowing the user to experiment with synthetic and experimental data sets, and different regularization strategies, in order to compare them and draw conclusions. The numerical effectiveness of the inversion procedure is demonstrated on synthetic and real datasets by using FDEMtools package. Zoom link <https://us02web.zoom.us/j/85165138386> Add event to Google calendar <https://calendar.google.com/event?action=TEMPLATE&tmeid=N2gxdW1xOGhjOTZsa2J…> -------------------------------------------------------------------- — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io

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Canceled event: Seminar on 17/11 (Francesco Tudisco) @ Tue Nov 17, 2020 11:00 - 12:00 (CET) (numpi@di.unipi.it)
by enrico.facca＠gmail.com 13 Nov '20

13 Nov '20

This event has been canceled. Title: [Numpi] Seminar on 17/11 (Francesco Tudisco) Speaker: Francesco Tudisco Affiliation: GSSI Time: Tuesday, 17/11/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: A tensor method for semi-supervised learning Semi-supervised learning is the problem of finding clusters in a graph or a point-clould dataset where we are given "few" initial input labels. Label Spreading (LS) is a standard technique for this problem, which can be interpreted as a diffusion process of the labels on the graph. While there are many variants of LS, nearly all of them are linear models which, for every node, only account for the information incoming from its direct neighbors. Recent work in network science has shown that in many graph algorithms a great advantage can be obtained when accounting directly for higher-order features. Such features may be built from the point-cloud data or the adjac... When: Tue Nov 17, 2020 11:00 – 12:00 Central European Time - Rome Joining info: Join with Google Meet https://meet.google.com/wtx-fpah-paw Calendar: numpi(a)di.unipi.it Who: * enrico.facca(a)gmail.com - organizer * numpi(a)di.unipi.it * f.durastante(a)na.iac.cnr.it * viviani(a)chalmers.se * leonardo.robol(a)unipi.it Invitation from Google Calendar: https://calendar.google.com/calendar/ You are receiving this courtesy email at the account numpi(a)di.unipi.it because you are an attendee of this event. To stop receiving future updates for this event, decline this event. Alternatively you can sign up for a Google account at https://calendar.google.com/calendar/ and control your notification settings for your entire calendar. Forwarding this invitation could allow any recipient to send a response to the organizer and be added to the guest list, or invite others regardless of their own invitation status, or to modify your RSVP. Learn more at https://support.google.com/calendar/answer/37135#forwarding

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Invitation: Seminar on 17/11 (Francesco Tudisco) @ Tue Nov 17, 2020 11:00 - 12:00 (CET) (numpi@di.unipi.it)
by enrico.facca＠gmail.com 13 Nov '20

13 Nov '20

You have been invited to the following event. Title: [Numpi] Seminar on 17/11 (Francesco Tudisco) Speaker: Francesco Tudisco Affiliation: GSSI Time: Tuesday, 17/11/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: A tensor method for semi-supervised learning Semi-supervised learning is the problem of finding clusters in a graph or a point-clould dataset where we are given "few" initial input labels. Label Spreading (LS) is a standard technique for this problem, which can be interpreted as a diffusion process of the labels on the graph. While there are many variants of LS, nearly all of them are linear models which, for every node, only account for the information incoming from its direct neighbors. Recent work in network science has shown that in many graph algorithms a great advantage can be obtained when accounting directly for higher-order features. Such features may be built from the point-cloud data or the adjac... When: Tue Nov 17, 2020 11:00 – 12:00 Central European Time - Rome Joining info: Join with Google Meet https://meet.google.com/wtx-fpah-paw Calendar: numpi(a)di.unipi.it Who: * enrico.facca(a)gmail.com - organizer * numpi(a)di.unipi.it * f.durastante(a)na.iac.cnr.it * viviani(a)chalmers.se * leonardo.robol(a)unipi.it Event details: https://calendar.google.com/calendar/event?action=VIEW&eid=M3Bmcm1maDdobmlk… Invitation from Google Calendar: https://calendar.google.com/calendar/ You are receiving this courtesy email at the account numpi(a)di.unipi.it because you are an attendee of this event. To stop receiving future updates for this event, decline this event. Alternatively you can sign up for a Google account at https://calendar.google.com/calendar/ and control your notification settings for your entire calendar. Forwarding this invitation could allow any recipient to send a response to the organizer and be added to the guest list, or invite others regardless of their own invitation status, or to modify your RSVP. Learn more at https://support.google.com/calendar/answer/37135#forwarding

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Reminder: Seminar on 03/11 (Angelo Casulli)
by Leonardo Robol 03 Nov '20

03 Nov '20

Dear all, this is just a reminder of today's seminar. Best, -- Leonardo. Speaker: Angelo Casulli Affiliation: SNS Time: Tuesday, 03/11/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: Rank-structured QR for Chebyshev rootfinding The computation of the roots of polynomials expressed in the Chebyshev basis has a lot of applications, for instance, it is useful in the computation of real roots of smooth functions. We present an algorithm for the rootfinding of Chebyshev polynomials based on an improvement of the QR iteration presented in [Eidelman, Y., Gemignani, L., and Gohberg, I., Numer. Algorithms , 47.3 (2008): pp. 253-273]. We introduce an aggressive early deflation strategy, and we show that the rank-structure allows to parallelize the algorithm avoiding data dependencies which would be present in the unstructured QR. The method exploits the particular structure of the colleague linearization to achieve quadratic complexity and linear storage requirements. The (unbalanced) QR iteration used for Chebyshev rootfinding does not guarantee backward stability on the polynomial coefficients, unless the vector of coefficients satisfy ||p|| ~ 1, an hypothesis which is almost never verified for polynomials approximating smooth functions. Even though the presented method is mathematically equivalent to the latter algorithm, we show that exploiting the rank structure allows to guarantee a small backward error on the polynomial, up to an explicitly computable amplification factor ɣ(p), which depends on the polynomial under consideration. We show that this parameter is almost always of moderate size, making the method accurate on several numerical tests, in contrast with what happens in the unstructured unbalanced QR. We also discuss the connection between the size of this amplification factor and the existence of a good balancing. This provides some insight on why the accuracy of our method is often very close to the balanced QR iteration. https://www.dm.unipi.it/webnew/it/seminari/rank-structured-qr-chebyshev-roo…

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Seminar on 03/11 (Angelo Casulli)
by Leonardo Robol 28 Oct '20

28 Oct '20

Speaker: Angelo Casulli Affiliation: SNS Time: Tuesday, 03/11/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: Rank-structured QR for Chebyshev rootfinding The computation of the roots of polynomials expressed in the Chebyshev basis has a lot of applications, for instance, it is useful in the computation of real roots of smooth functions. We present an algorithm for the rootfinding of Chebyshev polynomials based on an improvement of the QR iteration presented in [Eidelman, Y., Gemignani, L., and Gohberg, I., Numer. Algorithms , 47.3 (2008): pp. 253-273]. We introduce an aggressive early deflation strategy, and we show that the rank-structure allows to parallelize the algorithm avoiding data dependencies which would be present in the unstructured QR. The method exploits the particular structure of the colleague linearization to achieve quadratic complexity and linear storage requirements. The (unbalanced) QR iteration used for Chebyshev rootfinding does not guarantee backward stability on the polynomial coefficients, unless the vector of coefficients satisfy ||p|| ~ 1, an hypothesis which is almost never verified for polynomials approximating smooth functions. Even though the presented method is mathematically equivalent to the latter algorithm, we show that exploiting the rank structure allows to guarantee a small backward error on the polynomial, up to an explicitly computable amplification factor ɣ(p), which depends on the polynomial under consideration. We show that this parameter is almost always of moderate size, making the method accurate on several numerical tests, in contrast with what happens in the unstructured unbalanced QR. We also discuss the connection between the size of this amplification factor and the existence of a good balancing. This provides some insight on why the accuracy of our method is often very close to the balanced QR iteration. https://www.dm.unipi.it/webnew/it/seminari/rank-structured-qr-chebyshev-roo…

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Reminder: Seminar on 20/10 (Simon Telen)
by Leonardo Robol 19 Oct '20

19 Oct '20

Dear all, this is just a reminder of tomorrow's seminar by Simon Telen. Best, -- Leonardo. Speaker: Simon Telen Affiliation: MPI Leipzig Time: Tuesday, 20/10/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: Solving Polynomial Systems via Truncated Normal Forms Systems of polynomial equations arise from many problems in applied mathematics. Solving such systems is considered a challenging computational problem. An important class of numerical solving methods converts the problem into a system of coupled eigenvalue problems. In order to perform this conversion one has to choose a representation for an algebra naturally associated to the equations. Standard choices (coming from Gröbner bases, border bases, resultants ...) may show some very bad, numerical behaviour, even for generic systems. Truncated normal form methods generalise all the aforementioned approaches and are designed to avoid these numerical issues. I will introduce the theory and give many examples. This is joint work with Bernard Mourrain and Marc Van Barel. https://www.dm.unipi.it/webnew/it/seminari/solving-polynomial-systems-trunc…

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Seminar on 20/10 (Simon Telen)
by Leonardo Robol 13 Oct '20

13 Oct '20

Speaker: Simon Telen Affiliation: MPI Leipzig Time: Tuesday, 20/10/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: Solving Polynomial Systems via Truncated Normal Forms Systems of polynomial equations arise from many problems in applied mathematics. Solving such systems is considered a challenging computational problem. An important class of numerical solving methods converts the problem into a system of coupled eigenvalue problems. In order to perform this conversion one has to choose a representation for an algebra naturally associated to the equations. Standard choices (coming from Gröbner bases, border bases, resultants ...) may show some very bad, numerical behaviour, even for generic systems. Truncated normal form methods generalise all the aforementioned approaches and are designed to avoid these numerical issues. I will introduce the theory and give many examples. This is joint work with Bernard Mourrain and Marc Van Barel. https://www.dm.unipi.it/webnew/it/seminari/solving-polynomial-systems-trunc…

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Seminar on 06/10 (Milo Viviani)
by Leonardo Robol 06 Oct '20

06 Oct '20

Dear all, below you find the first announcement for the NumPI seminars. The seminar will be next week on Tuesday, and will be online using the conference platform available at the math department. You find the link below (which will stay the same for all conferences, assuming it works well). When entering the conference you will be asked if you want to only listen or to join with microphone; I suggest you choose the latter: you will be muted anyway after joining, but will be able to ask questions at the end if you wish. Best wishes, -- Leonardo. Speaker: Milo Viviani Affiliation: Scuola Normale Superiore, Pisa Time: Tuesday, 06/10/2020, 11:00 Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 Title: Symplectic methods for isospectral flows and 2D ideal hydrodynamics The numerical solution of non-canonical Hamiltonian systems is an active and still growing field of research. At the present time, the biggest challenges concern the realization of structure preserving algorithms for differential equations on infinite dimensional manifolds. Several classical PDEs can indeed be set in this framework, and in particular the 2D hydrodynamical Euler equations. In this talk, I will present some results I have obtained during my PhD studies. In particular, I will show how to derive a new class of numerical schemes for Hamiltonian and non-Hamiltonian isospectral flows, in order to solve the 2D hydrodynamical Euler equations. The use of a conservative scheme has revealed new insights in the 2D ideal hydrodynamics, showing clear connections between geometric mechanics, statistical mechanics and integrability theory. https://www.dm.unipi.it/webnew/it/seminari/symplectic-methods-isospectral-f…

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2 PhD positions at Charles University, Prague
by Paola BOITO 28 Sep '20

28 Sep '20

Cari tutti, su richiesta di Stefano Pozza inoltro volentieri questo annuncio per 2 posizioni di PhD e una come postdoc a Praga. Un caro saluto, Paola *************************************** *2 Ph.D. Positions*, Krylov methods and ODE approximation. Two Ph.D. positions are available within the framework of the Primus Research Programme: "A Lanczos-like Method for the Time-Ordered Exponential" at the Faculty of Mathematics and Physics, Charles University, Prague. The four years of Ph.D. studies will be done under the supervision of Dr. Stefano Pozza (PI of the project) in the Department of Numerical Mathematics. The department offers an international environment at one of the top universities in the Czech Republic, and the oldest university in Central Europe. The students will also have the opportunity to work with external collaborators from France, Italy, and the UK. The applicants must hold a Master's degree by the start date of Spring 2021 (to be announced) and should have a strong interest in numerical linear algebra and numerical analysis. Knowledge of Matlab or other programming languages is necessary. Applicants will have to prove their English language level by passing an exam (it is possible to waive the examination under some conditions, see https://www.mff.cuni.cz/en/admissions/admission-procedure-in-phd-programmes…) Application deadline: *November 9, 2020.* More information and application instructions: https://www.starlanczos.cz/open-positions

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NumPI Seminars
by Leonardo Robol 21 Sep '20

21 Sep '20

Dear all, in this semester we won't be able to attend seminars as usual, by physically meeting in a seminar room (or at least, not as easily as it used to be). I had a chat with some of you, and there is some interest in having an online version of the usual seminar series. So here is some practical information: -) The first seminar will be in the week 5/10 - 9/10; I prepared a Doodle [1] for choosing the best possible date, considering most of us will be teaching. Please fill it by the end of this week, and consider that the chosen day of the week will be the same for (most of) the next seminars as well. -) Our first speaker will be Milo Viviani, which is starting a postdoc at SNS with Michele Benzi. Title and abstract will follow in the next days, along with the chosen date and further details. -) I am inclined in using the streaming platform that we have at the department of Mathematics [2], hopefully it will work fine. Otherwise, we will have a backup plan :) More details on this will follow as well. We will have a few internal speakers, and a few "invited" ones; in case you wish to give a talk please write me an e-mail, so we can allocate a slot. See you soon (online or in person)! Best wishes, -- Leonardo. [1] https://doodle.com/poll/qtftd9zsxn6hivp6 [2] https://hausdorff.dm.unipi.it/

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Serie di seminari CommNLA
by Leonardo Robol 07 Sep '20

07 Sep '20

Cari tutti, è cominciata oggi una serie di seminari di algebra lineare numerica pensata per i chi sia all'inizio della carriera accademica, con l'intento di recuperare l'ambiente di discussione informale delle conferenze a cui non abbiamo potuto partecipare. Se siete interessati potete registrarvi [1], in modo da ricevere gli annunci dei seminari; i primi due sono stati oggi (scusate il ritardo!) e continueranno ogni lunedì alle 15.00; si tratta di due seminari da 30 minuti, quelli di oggi saranno presto disponibili su Youtube [2]. Dopo i talk, si può partecipare ad un "coffee-break virtuale" su gather.town [3], dove è possibile interagire con gli speaker e gli altri partecipanti in una sorta di videogioco-conferenza. A presto, -- Leonardo. [1] https://sites.google.com/view/commnla/ [2] https://www.youtube.com/channel/UCSlAhBOIY68IWLxpPUFHuSQ [3] https://gather.town/

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Fwd: Online seminar on Linear Algebra and Operator Theory
by Leonardo Robol 04 Jun '20

04 Jun '20

Buongiorno, inoltro questo annuncio di una serie di seminari online su algebra lineare e teoria degli operatori, che potrebbe essere di interesse per molti di noi. A presto, -- Leonardo. > -------- Forwarded Message -------- > Subject: Online seminar on Linear Algebra and Operator Theory > Date: Mon, 1 Jun 2020 12:54:12 +0000 > From: Oselot <oselot(a)uj.edu.pl> > To: Ran, A.C.M. <a.c.m.ran(a)vu.nl>, Michał Wojtylak < > michal.wojtylak(a)uj.edu.pl>, via the vacation program < > mehl(a)math.tu-berlin.de> > > > Dear Colleague, > > We would like to bring your attention to the following event: > > Online Seminar on Linear Algebra and Operator Theory (Oselot) > > that takes place weekly, on Thursday, 15:00 CEST, 45 minutes talk + > 15 minutes discussion. > > We will be happy if you could join us. > You are welcome to register at any time by sending an email to oselot > [at] uj.edu.pl, we will send you weekly a code to the zoom event. > > Please feel free to distribute this invitation to your colleagues, > PhD students and postdocs. > > With kind regards, > Christian Mehl > Andre Ran > Michal Wojtylak > > > > The upcoming lectures: > > > 04-06 Sanne ter Horst > Schur coupling and related Banach space operator relations > > 11-06 NO SEMINAR > > 18-06 Volker Mehrmann > The relation between positive realness, passivity and port- > Hamiltonicity of linear dynamical systems. > > 25-06 Froilan Dopico > > Sets of matrix polynomials with bounded rank and degree and their > generic eigenstructures > > 02-07 Thomas Berger > > Funnel control for the Fokker-Planck equation > > 09-07 Shreemayee Bora (title TBA) > > SUMMER BREAK > > In the new semester we start with the following, tentative, set of > speakers > > 17-09 Jonathan Partington > 24-09 Marek Bożejko > 01-10 Michael Dritschel > 08-10 Andrii Dmytryshyn > 15-10 Federico Poloni > 22-10 Christian Budde

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Seminari online
by Leonardo Robol 20 Apr '20

20 Apr '20

Carissimi, date le restrizioni attualmente in vigore, non potremo ovviamente continuare con i seminari numerici. Vi segnalo quest'ottima alternativa [1]; è possibile effettuare la registrazione sul sito e seguire poi i seminari online. Il primo seminario si terrà il 29/4 (mercoledì della settimana prossima), e sarà tenuto da Nick Higham, che parlerà di precisione mista in algebra lineare numerica. Saluti, -- Leonardo Robol. [1] https://sites.google.com/view/e-nla/home

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Seminar on 04/03 (Daniel Szyld)
by Leonardo Robol 03 Mar '20

03 Mar '20

Speaker: Daniel Szyld Affiliation: Temple University Wednesday, 04/03/2020, 11:00, Aula Tonelli, SNS. Title: Efficient iterative methods for the solution of Generalized Lyapunov Equations: Block vs. point Krylov projections, and other controversial decisions. There has been a flurry of activity in recent years in the area of solution of matrix equations. In particular, a good understanding has been reached on how to approach the solution of large scale Lyapunov equations. An effective way to solve Lyapunov equations of the form $A^T X + XA + C^T C = 0$, where A and X are n×n, is to use Galerkin projection with appropriate extended or rational Krylov subspaces. These methods work in part because the solution is known to be symmetric positive definite with rapidly decreasing singular values, and therefore it can be approximated by a low rank matrix X_k = Z_k Z_k^T. Thus the computations are performed usually with storage which is lower rank, i.e., much lower than order of n^2 . Generalized Lyapunov equations have additional terms. In this talk, we concentrate on equations of the following form $$ A^T X + XA + \sum_{j = 1}^m N_j X N_j^T + C^T C = 0, $$ Such equations arise for example in stochastic control. In the present work, we propose a return to classical iterative methods, and consider instead stationary iterations. The classical theory of splittings applies here, and we present a new theorem on the convervegence when the linear system at each step is solved inexactly. Several theoretical and computational issues are discussed so as to make the iteration efficient. Numerical experiments indicate that this method is competitive vis-à- vis the current state-of-the-art methods, both in terms of computational times and storage needs. This is joint work with Stephen D. Shank and Valeria Simoncini. https://www.dm.unipi.it/webnew/it/seminari/efficient-iterative-methods-solu…

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Seminar on 29/01 (Simona Perotto)
by Leonardo Robol 29 Jan '20

29 Jan '20

Speaker: Simona Perotto Affiliation: Politecnico di Milano Wednesday, 29/01/2020, 11:00, Aula Tonelli, SNS. Title: Topology optimization: a new algorithm based on anisotropic mesh adaptation Topology optimization provides useful mathematical tools for the design of optimal (e.g., minimizing the compliance) structures for assigned loads and boundary conditions, and under suitable constraints (e.g., a given fraction of the initial volume). The SIMP (Solid Isotropic Material with Penalization) method represents one of the most investigated approaches for topology optimization. It belongs to the family of density-based methods, where an auxiliary (unknown) scalar field (the density), taking values between zero (void) and one (material), is adopted to describe the final layout of the optimized structure. SIMP exhibits many drawbacks, among which the non-uniqueness of the optimal structure and issues related to the adopted discretization for the optimization problem (e.g., checkerboard, greyscale, and staircase effects). In this talk, we present the new algorithm SIMPATY (SIMP+AdaptiviTY) which enriches the basic SIMP method with anisotropic mesh adaptivity to alleviate some of the above- mentioned issues. After introducing the mathematical background, we provide a detailed description of the SIMPATY algorithm and we verify its performance on benchmarks as well as on more challenging structure configurations. https://www.dm.unipi.it/webnew/it/seminari/topology-optimization-new-algori…

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Seminar on 20/01 (Fernando De Terán)
by Leonardo Robol 20 Jan '20

20 Jan '20

Speaker: Fernando De Terán Affiliation: Universidad Carlos III de Madrid Time: Monday, 20/01/2020, 14:00 Place: Aula Magna, Dipartimento di Matematica. Title: Flanders’ theorem for many matrices under commutativity assumptions Given two matrices $A \in C^{m \times n}$ and $B \in C^{n \times m}$ , it is known [1] that the Jordan canonical form of AB and BA can only differ in the sizes of the Jordan blocks associated with the eigenvalue zero, and the difference in the size of any two corresponding blocks is, at most, 1. Moreover, this change is exhaustive, in the sense that given two ordered lists of numbers such that the corresponding elements differ at most by 1, then there are two matrices A, B such that the fist list is the list of sizes of Jordan blocks associated with 0 in AB and the second one is the list of sizes of Jordan blocks associated with 0 in BA. The motivation of this work is the question: What happens with products of more than two matrices? First, we will see that, if we do not impose any restriction, the products ABC and CBA may have completely different eigenvalues. Therefore, some conditions must be imposed to the factors in order to be able to relate the Jordan canonical forms of any two products. By imposing some natural commutativity assumptions, we analyze the relationship between the Jordan canonical form of products, in different orders, of k square matrices $A_1, ..., A_k$. In particular, we study permuted products of $A_1, ..., A_k$ under the assumption that the graph of non-commutativity relations is a forest. Under this condition, we show that the Jordan structure of all nonzero eigenvalues is the same for all permuted products. For the eigenvalue zero, we obtain an upper bound on the difference between the sizes of Jordan blocks for any two permuted products, and we show that this bound is attainable. For k = 3 we show that, moreover, the bound is exhaustive. This is joint work with Ross A. Lippert, Yuji Nakatsukasa, and Vanni Noferini. https://www.dm.unipi.it/webnew/it/seminari/flanders%E2%80%99-theorem-many-m…

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Seminar on 11/12 (Vanni Noferini)
by Leonardo Robol 11 Dec '19

11 Dec '19

Speaker: Vanni Noferini Affiliation: Aalto University, Finland Time: Wednesday, 11/12/2019, 11:00 Place: Aula Seminari, Dipartimento di Matematica. Title: Wilkinson's bus: weak condition numbers, with applications (Joint work with Martin Lotz) Simple eigenvalues of singular matrix polynomials have infinite condition number. However, vanilla eigensolvers (blind to the singular structure) are often able to compute these eigenvalues to machine precision. We propose and analyse a more sophisticated theory of condition, with higher predicting power than the existing ones. Don't miss this talk if you would like to hear the solution of the mystery of the ill posed eigenvalue problems that are in practice solved with remarkable accuracy! https://www.dm.unipi.it/webnew/it/seminari/wilkinsons-bus-weak-condition-nu…

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Cena di Natale
by Leonardo Robol 04 Dec '19

04 Dec '19

Carissimi, anche quest'anno vorremmo provare a organizzare una cena prima di Natale; si pensava di organizzarla con un po' di anticipo in modo da poter includere anche gli ospiti che abbiamo in dipartimento in questo periodo (i.e., Vanni e Massimiliano). Ho parlato solo con alcuni di voi, e ci sarebbe abbastanza convergenza per il 9, 10 oppure l'11 di dicembre (lunedì, martedì, o mercoledì della settimana prossima). Se pensate di partecipare, vi chiederei di riempire il Doodle che trovate a questo indirizzo [1], possibilmente entro un paio di giorni così che poi possa prenotare. Per il momento c'è un certo supporto per rispolverare un classico e tornare a Montemagno (ammesso di trovare posto), ma ovviamente proposte per la location sono sembre bene accette! L'invito è esteso a numerici e simpatizzanti, chiunque abbia piacere a partecipare si può considerare incluso. A presto! -- Leonardo. [1] https://doodle.com/poll/fg22d7ezy7ziwcy2

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Seminar on 04/12 (Stefano Massei)
by Leonardo Robol 27 Nov '19

27 Nov '19

Speaker: Stefano Massei Affiliation: EPF Lausanne, Switzerland Time: Wednesday, 04/12/2019, 11:00 Place: Sala Seminari Est, Dipartimento di Informatica. Title: Rational Krylov for Stieltjes matrix functions: convergence and pole selection Evaluating the action of a matrix function on a vector, that is x = f(M)v, is an ubiquitous task in applications. When the matrix M is large, subspace projection method, such as the rational Krylov method, are usually employed. In this work, we provide a quasi-optimal pole choice for rational Krylov methods applied to this task when f(z) is either Cauchy-Stieltjes or Laplace-Stieltjes (or, which is equivalent, completely monotonic) for a positive definite matrix M. Then, we consider the case when the argument M has the Kronecker structure M = I⊗A - B^T⊗I, and is applied to a vector obtained vectorizing a low-rank matrix. This finds application, for instance, in solving fractional diffusion equation on rectangular domains. We introduce an error analysis for the numerical approximation of x. Pole choices and explicit convergence bounds are given also in this case. https://www.dm.unipi.it/webnew/it/seminari/rational-krylov-stieltjes-matrix…

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Seminar on 27/11 (Gerald Williams)
by Leonardo Robol 27 Nov '19

27 Nov '19

Speaker: Gerald Williams Affiliation: University of Essex, UK Time: Wednesday, 27/11/2019, 11:00 Place: Aula Magna, Dipartimento di Matematica Title: The role of circulant matrices in the study of cyclically presented groups A circulant matrix is a square matrix in which each row is obtained from its predecessor by a cyclic shift by one column. A cyclically presented group is one that is defined by a group presentation (ie a description of a group in terms of generators and defining relations) that admits a similar cyclic symmetry. Prominent examples are the Fibonacci groups, where the presentations' defining relations mimic the Fibonacci recurrence relation. Questions that arise when studying cyclically presented groups ask when such a group is finite or perfect, when it is 3-manifold group or knot group; if so, what more can we say about the group. Knowledge of the determinant, rank, and the Smith normal form of a related circulant matrix can help to answer these questions. In this talk I will discuss how well-known properties of circulant matrices have been used to gain insight into the structure of cyclically presented groups, and discuss recent and ongoing work with Vanni Noferini that is advancing the theory to provide new tools for studying such groups. https://www.dm.unipi.it/webnew/it/seminari/role-circulant-matrices-study-cy…

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Seminar on 20/11 (Enrico Facca)
by Leonardo Robol 19 Nov '19

19 Nov '19

Speaker: Enrico Facca Affiliation: Scuola Normale Superiore, Pisa Time: Wednesday, 20/11/2019, 11:00 Place: Aula Tonelli, SNS Title: A bio-inspired optimization tool, the Dynamic Monge-Kantorovich model. Numerical solutions and applications In this talk I will present the Dynamical Monge-Kantorovich model, a PDE system coupling an elliptic equation with a diffusion coefficient that change in time according to a non-linear dynamics. The steady state of this system has been related to the different Optimal Transport problems, offering an efficient numerical scheme for their solution. We will explore some examples of application, like identification of the Cut-Locus of a point on manifold and the study of complex natural network. The simplicity of the model allows simple but effective transformations of its core equations, that have been shown to be connected with different optimization problems, such as the Basis Pursuit Problem and the Shape Optimization Problem. https://www.dm.unipi.it/webnew/it/seminari/bio-inspired-optimization-tool-d…

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Lectio Luca Trevisan, "A Theory of Spectral Clustering"
by Federico Poloni 17 Nov '19

17 Nov '19

Segnalo la presenza di questo colloquio, che non fa parte della nostra serie di seminari ma ha un tema che potrebbe essere di interesse per gli iscritti alla lista. È una "lectio magistralis" che fa parte delle celebrazioni per i 50 anni del corso di laurea in informatica. Si terrà nell'aula magna del polo Pontecorvo (edificio E) lunedì 18 novembre alle 15:30. Cordialmente, -federico -------- Forwarded Message -------- Subject: [Dipartimento.di] Lectio Luca Trevisan Date: Fri, 15 Nov 2019 09:55:55 +0100 From: Gian Luigi Ferrari <gian-luigi.ferrari(a)unipi.it> To: CDD <cdd(a)di.unipi.it>, dipartimento(a)di.unipi.it Lo avevo comunicato in consiglio ma mi sono scordato di mandarlo via mail. Rimedio Title: A Theory of Spectral Clustering Speaker: Luca Trevisan Abstract: Spectral clustering algorithms find clusters in a given network by exploiting properties of the eigenvectors of matrices associated with the network. As a first step, one computes a spectral embedding, that is a mapping of nodes to points in a low-dimensional real space; then one uses geometric clustering algorithms such as k-means to cluster the points corresponding to the nodes. Such algorithms work so well that, in certain applications unrelated to network analysis, such as image segmentation, it is useful to associate a network to the data, and then apply spectral clustering to the network. In addition to its application to clustering, spectral embeddings are a valuable tool for dimension-reduction and data visualization. The performance of spectral clustering algorithms has been justified rigorously when applied to networks coming from certain probabilistic generative models. A more recent development, which is the focus of this lecture, is a worst-case analysis of spectral clustering, showing that, for every graph that exhibits a certain cluster structure, such structure can be found by geometric algorithms applied to a spectral embedding. Such results generalize the graph Cheeger’s inequality (a classical result in spectral graph theory), and they have additional applications in computational complexity theory and in pure mathematics. ——— Bio: Luca Trevisan is a professor of Computer Science at Bocconi University. Luca studied at the Sapienza University of Rome, he was a post-doc at MIT and at DIMACS, and he was on the faculty of Columbia University, U.C. Berkeley, and Stanford, before returning to Berkeley in 2014 and, at long last, moving back to Italy in 2019. Luca's research is in theoretical computer science, and it is focused on computational complexity and graph algorithms. Luca received the STOC'97 Danny Lewin (best student paper) award, the 2000 Oberwolfach Prize, and the 2000 Sloan Fellowship. He was an invited speaker at the 2006 International Congress of Mathematicians. He is a recipient of a 2019 ERC Advanced Grant. ______________________________________________ Dipartimento.di mailing list Dipartimento.di(a)listgateway.unipi.it http://listgateway.unipi.it/mailman/listinfo/dipartimento.di

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Seminar on 13/11 (Massimiliano Fasi)
by Leonardo Robol 12 Nov '19

12 Nov '19

Speaker: Massimiliano Fasi Affiliation: Department of Mathematics, The University of Manchester Time: Wednesday, 13/11/2019, 11:00 Place: Aula Seminari, Dipartimento di Matematica Title: Handling the conditioning of extreme-scale matrices In order to assess experimentally the stability of algorithms for the solution of systems of linear equations, it is typically desirable to have a certain degree of control over the condition number of the test matrices being used. If the tests are being performed at scale (e.g., in an HPL benchmark run for a TOP500 submission), it is necessary to ensure that generating the test data will take up only a negligible portion of the overall execution time required to solve the linear system. We develop two new techniques that satisfy these requirements and can be used to efficiently construct extremely large matrices with preassigned 2-norm condition number. Focusing on distributed memory environments, we discuss how these can be implemented in a communication-avoiding fashion. https://www.dm.unipi.it/webnew/it/seminari/handling-conditioning-extreme-sc…

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Colloquio della Classe di Scienze - Alfio Quarteroni
by Leonardo Robol 23 Oct '19

23 Oct '19

Dear all, Alfio Quarteroni will give a presentation at SNS next Wednesday at 15:00, which might be of interest to some of you. The topic is "Taking mathematics to heart"; you can find more information, including venue and abstract, on the SNS website [1]. [1] https://www.sns.it/it/evento/taking-mathematics-to-heart Best wishes, Leonardo Robol.

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Seminari autunnali NumPI
by Leonardo Robol 09 Oct '19

09 Oct '19

Carissimi, prossimamente si terranno alcuni seminari numerici, al Dipartimento di Matematica / Informatica e in Normale, come l'anno scorso. Invito chi di voi fosse potenzialmente interessato a partecipare a compilare il Doodle [1], in modo da poter scegliere un giorno ed un'ora che non coincida con i vostri impegni / lezioni (o almeno, che lo faccia per il minor numero possibile di persone). Per comodità, il Doodle è per date della prossima settimana, ma _non ci sarà_ davvero un seminario la settimana prossima! Probabilmente i primi saranno a fine ottobre / inizio di novembre. Grazie, a presto. [1] https://doodle.com/poll/5p2fm3brdrnu6h4f -- Leonardo Robol <leonardo.robol(a)unipi.it>

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Seminar on 04/07 (Federico Poloni)
by Leonardo Robol 04 Jul '19

04 Jul '19

Speaker: Federico Poloni Affiliation: Department of Computer Science, University of Pisa Time: Thursday, 04/07/2019 Place: Aula Magna, Dipartimento di Matematica Title: Principal pivot transforms, quasidefinite matrices, and matrix equations Principal pivot transforms are maps between matrices that generalize, in some sense, Schur complementation and inversion. They are a somewhat counterintuitive but powerful tool that allows one to reinterpret Gaussian elimination-type algorithms in a different framework. We will show how they can deal successfully with various kinds of matrices in a structure-preserving way; this includes (weakly) quasi-definite matrices, i.e., symmetric matrices with two complementary diagonal blocks of opposite definiteness, as well as Hamiltonian/symplectic matrices. We will then present an algorithm to solve dense algebraic Riccati equations in a factored form, which relies on these transforms as a basic building block.

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Seminar on 25/06 (Michael Overton)
by Leonardo Robol 24 Jun '19

24 Jun '19

Speaker: Michael Overton Affiliation: New York University Time: Wednesday, 25/06/2019, 11:00 Place: Aula Mancini, SNS Title: Crouzeix's conjecture Crouzeix's conjecture is among the most intriguing developments in matrix theory in recent years. Made in 2004 by Michel Crouzeix, it postulates that, for any polynomial p and any matrix A, ||p(A)|| <= 2 max(|p(z)|: z in W(A)), where the norm is the 2-norm and W(A) is the field of values (numerical range) of A, that is the set of points attained by v*Av for some vector v of unit length. Crouzeix proved in 2007 that the inequality above holds if 2 is replaced by 11.08, and recently this was greatly improved by Palencia, replacing 2 by 1+sqrt(2). Furthermore, it is known that the conjecture holds in a number of special cases, including n=2. We use nonsmooth optimization to investigate the conjecture numerically by locally minimizing the “Crouzeix ratio”, defined as the quotient with numerator the right-hand side and denominator the left-hand side of the conjectured inequality. We also present local nonsmooth variational analysis of the Crouzeix ratio at conjectured global minimizers. All our results strongly support the truth of Crouzeix’s conjecture.

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Seminar on 05/06 (Leonardo Robol)
by Leonardo Robol 03 Jun '19

03 Jun '19

Dear all, I am sorry for the delay in this announcement, I was planning to send it before, but it slipped off my mind. Everybody is welcome to attend, as usual. Speaker: Leonardo Robol Affiliation: Department of Mathematics, University of Pisa Time: Wednesday, 05/06/2019 Place: Aula Riunioni, Dipartimento di Matematica Title: Rank structures in matrix equations and matrix functions Low-rank matrices (and tensors) appear often in applications, and this can be exploited in several ways to treat large scale problems that would be otherwise unfeasible. It has been known since a long time that in some applications, such as the solution of the Sylvester equation AX + XB + C = 0, working with low-rank C often leads to a solution X which is full rank, but can be efficiently approximated by a low-rank matrix. This can be used, among other things, in solving PDEs defined by separable operators, such as the 2D Laplace operator on rectangular domains. We briefly review some of these results, and the connection with some rational approximation problems. We show that these structures appear in a multitude of interesting cases. For instance, the same properties can be found when modifying the coefficients of linear matrix equation by performing low-rank updates to their coefficients, and the theory can be extended to more general matrices which have off-diagonal blocks of low-rank. Time permitting, we discuss some recent developments that allow to prove the existence of a low-rank structures in the action of functions of matrices that have a Kronecker sum structure, such as x = f (A⊗I + B^T⊗I)v, for particularly structured vector v. An efficient algorithm for the approximation of the vector x, reshaped in matrix form, is given. This founds applications in extending the ideas used for the Laplace operator and 2D PDEs to more general nonlocal operators, such as the fractional Laplacian.

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Seminar on 11/04 (Fabio Carrara)
by Leonardo Robol 11 Apr '19

11 Apr '19

Speaker: Fabio Carrara Affiliation: ISTI-CNR, Pisa Time: Thursday, 11 April 2019, h. 14:00 Place: Aula Riunioni, Dipartimento di Matematica Title: Neural networks for image understanding: methods, limitations, and new frontiers Vision is natural and easy for living beings, while it is incredibly complex to be replicated in machines. In the last 40 years, a lot of work in Computer Vision has been spent trying to model and implement visual perception manually, with slow improvements over time. However, in the last decade, deep neural networks revolutionized this field by automatically learning complex models for vision from huge amounts of data, thus relieving the practitioners from defining and extracting complex visual features that would require a lot of manual effort to find. In this talk, we will make a journey into neural networks for computer vision focusing on tasks in which they shine, that is image recognition and understanding. We will cover the most successful neural network formulation for visual data, that is the convolutional neural network, from the basics to recent architectures, while pinpointing current limitations in the field. In conclusion, we will discuss novel neural network architectures, such as continuous ODE-defined models, that have been recently proposed and provide new research directions.

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Seminar on 08/04 (Raf Vandebril)
by Leonardo Robol 08 Apr '19

08 Apr '19

Speaker: Raf Vandebril Affiliation: Department of Computer Science, KU Leuven Time: Monday, 08 April 2019, h. 14:00 Place: Aula Seminari, Dipartimento di Matematica Title: Structures, Gramians, and Krylov Krylov methods are typically used for transforming large scale prolems and matrices to matrices of a manageable size. Krylov inspired algorithms are based on the principle: project - solve - lift. In this talk we will focus on the projection step, the orthogonal bases involved, and the structured of the resulting projection. Two bases are needed for the projection: a basis for a search Krylov subspace, say V, and another basis for the constraint Krylov subspace, name it W. For a matrix A, the projected small to medium sized matrix will be W^*AV. There is now a wide variety of possibilities for constructing the matrices W and V. We could go from classical Krylov to extended and rational Krylov subspaces. But we could also attempt to construct subspaces with variants of the matrix A, such as for instance its inverse, its conjugate transpose, or the inverse of its conjugate transpose. In this lecture we will examine some of these possibilities. A general framework is proposed in which we will touch upon the following aspects: biorthogonal (rational) Krylov, CMV factorizations, non-unitary CMV factorizations, quasiseparable Hessenberg matrices, Hankel and Toeplitz Gramians.

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Seminar on 12/04 (James Nagy)
by Leonardo Robol 04 Apr '19

04 Apr '19

Speaker: James Nagy Affiliation: Department of Mathematics, Emory University Time: Friday, 12 April 2019, h. 11:00 Place: Aula Mancini, SNS Title: MATLAB Tools for Large-Scale Linear Inverse Problems Inverse problems arise in a variety of applications: image processing, finance, mathematical biology, and more. Mathematical models for these applications may involve integral equations, partial differential equations, and dynamical systems, and solution schemes are formulated by applying algorithms that incorporate regularization techniques and/or statistical approaches. In most cases these solutions schemes involve the need to solve a large-scale ill-conditioned linear system that is corrupted by noise and other errors. In this talk we describe and demonstrate capabilities of a new MATLAB software package that consists of state-of-the-art iterative methods for solving such systems, which includes approaches that can automatically estimate regularization parameters, stopping iterations, etc., making them very simple to use. Thus, the package allows users to easily incorporate into their own applications (or simply experiment with) different iterative methods and regularization strategies with very little programming effort. On the other hand, sophisticated users can also easily access various options to tune the algorithms for certain applications. Moreover, the package includes several test problems and examples to illustrate how the iterative methods can be used on a variety of large-scale inverse problems. The talk will begin with a brief introduction to inverse problems, discuss considerations that are needed to compute an approximate solution, and describe some details about new efficient hybrid Krylov subspace methods that are implemented in our package. These methods can guide users in automatically choosing regularization parameters, and can be used to enforce various regularization schemes, such as sparsity. We will use imaging examples that arise in medicine and astronomy to illustrate the performance of the methods. This is joint work with Silvia Gazzola (University of Bath) and Per Christian Hansen (Technical University of Denmark).

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Seminar on 04/04 (Peter Benner)
by Leonardo Robol 22 Mar '19

22 Mar '19

Speaker: Peter Benner Affiliation: Max Planck Institute for Dynamics of Complex Technical Systems Time: Thursday, 04 April 2019, h. 15:00 Place: Sala Seminari Ovest, Dipartimento di Informatica Title: Low-rank tensor methods for PDE-constrained optimization under uncertainty We discuss optimization and control of unsteady partial differential equations (PDEs), where some coefficient of the PDE as well as the control may be uncertain. This may be due to the lack of knowledge about the exact physical parameters, like material properties describing a real-world problem (''epistemic uncertainty'') or the inability to apply a computed optimal control exactly in practice. Using a stochastic Galerkin space-time discretization of the optimality system resulting from such PDE-constrained optimization problems under uncertainty leads to large-scale linear or nonlinear systems of equations in saddle point form. Nonlinearity is treated with a Picard-type iteration in which linear saddle point systems have to be solved in each iteration step. Using data compression based on separation of variables and the tensor train (TT) format, we show how these large-scale indefinite and (non)symmetric systems that typically have 10⁸ to 10¹⁵ unknowns can be solved without the use of HPC technology. The key observation is that the unknown and the data can be well approximated in a new block TT format that reduces complexity by several orders of magnitude. As examples, we consider control and optimization problems for the linear heat equation, the unsteady Stokes and Stokes-Brinkman equations, as well as the incompressible unsteady Navier-Stokes equations. The talk surveys the results published in [1,2] and provides new results for the Navier-Stokes case. [1] P. Benner, A. Onwunta, M. Stoll, Block-diagonal preconditioning for optimal control problems constrained by PDEs with uncertain inputs, SIAM Journal on Matrix Analysis and Applications, 37(2):491--518, 2016. [2] P. Benner, S. Dolgov, A. Onwunta, M. Stoll, Low-rank solvers for unsteady Stokes-Brinkman optimal control problem with random data, Computer Methods in Applied Mechanics and Engineering, 304:26--54, 2016.

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