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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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