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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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