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276 discussions

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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