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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 05 Oct '22

05 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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