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Annuncio di Seminario
by Leonardo Robol 13 Mar '19

13 Mar '19

Dear all, on Monday next week Carla Hernando, a PhD student visiting the department of Computer Science for three months, will give a seminar on her research. You are all welcome to attend, the abstract is attached below. Best wishes, -- Leonardo. Speaker: Carla Hernando Affiliation: UC3M, Madrid Time: Monday, 18 March 2019, h. 14:00 Place: Sala Seminari, Dipartimento di Matematica Title: Sparse linearizations and (sparse) structured ell-ifications The talk is divided in two main parts. The first one is focused on (generalized) companion pencils, which are strong linearizations and they present a template involving no arithmetic operations at all. In addition, we are mainly interested in sparse (generalized) companion pencils and then, we determine the smallest number of nonzero entries of a particular class of companion pencils. In the case of generalized companion pencils, we should impose natural conditions on its entries. In the second one, a family of structured block Kronecker ell-ifications will be introduced. This family has the particular structure of a strong block minimal bases polynomial, introduced in [1]. Furthermore, we have introduced two new subfamilies of structured block Kronecker ell-ifications where not only there is no duplication of the coefficients of the polynomial, but also the degree-ell polynomial is sparse. This is joint work with Fernando de Terán (UC3M, Spain), my thesis director. [1] F.M.Dopico, J.Pérez, P.Van Dooren. Block minimal bases ell-ifications of matrix polynomials. Linear Algebra Appl., 562 (2019), 163-204

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Annuncio di Seminario
by Leonardo Robol 13 Mar '19

13 Mar '19

Dear all, the next seminar will be the next week on Thursday (so _not_ tomorrow), and will be hosted at SNS. You find the abstract below. See you there, Best, -- Leonardo. Speaker: Michiel Hochstenbach Affiliation: TU Eindhoven Time: Thursday, 14 March 2019, h. 15:00 Place: Aula Tonelli, SNS Title: Solving polynomial systems by determinantal representations Zeros of a polynomial, p(x)=0, are often determined by computing the eigenvalues of a companion matrix: a matrix A which satisfies det(A-xI)=p(x). In this talk we consider polynomial systems, in particular in 2 variables: p(x,y)=0, q(x,y)=0. We look for a determinantal representation for such a bivariate polynomial: matrices A, B, C such that det(A-xB-yC)=p(x,y). This means that we can compute the zeros of the system by solving a 2-parameter eigenvalue problem. This approach, which already goes back to a theorem by Dixon in 1902, leads to fast solution methods, as well as a multitude of interesting open research questions. This is mainly joint work with Bor Plestenjak (Ljubljana), and additionally several colleagues in algebra, among which Ada Boralevi (Torino).

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Annuncio di Seminario
by Leonardo Robol 27 Feb '19

27 Feb '19

Speaker: Fabio Durastante Affiliation: University of Pisa Time: Thursday, 28 February 2019, h. 14:00 Place: Sala Seminari Est, Dipartimento di Informatica Title: The Krylov--Jacobi method: functions of matrices for fractional partial differential equations In this talk I discuss briefly some computational issues concerning a Krylov method of rational type for the computation of certain matrix functions occurring in the solution of fractional partial differential equations. Specifically, a new set of poles for the computation of the following functions of symmetric positive definite matrices is introduced: - fractional power, $f(z) = z^{-\alpha/2}$, - resolvent of fractional power, $f(z) = (1+\nu z^{\alpha/2})^{-1}$. The underlying approach permits to efficiently semidiscretize the fractional Laplacian operator on non Cartesian/regular grids exploiting either Finite Differences, Finite Elements, or Finite Volumes schemes, and to employ any appropriate linear multistep method for marching in time. Numerical experiments on some fractional partial differential equation model problems and comparisons with other methods, including other popular rational Krylov methods, confirm that the proposed approach is promising. This is a joint work with: L. Aceto, D. Bertaccini, and P. Novati.

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Seminari di Analisi Numerica - seconda sessione
by Leonardo Robol 19 Feb '19

19 Feb '19

Cari tutti, durante il secondo semestre ci saranno altri seminari nel ciclo di analisi numerica, in continuazione con quelli del primo semestre. Come per l'ultima volta, chiederei a chi è interessato a partecipare di compilare il Doodle [1], per permetterci di scegliere un orario durante la settimana che accontenti il maggior numero di persone. Nei prossimi giorni cominceremo a stendere il calendario, e dai primi di marzo dovrebbero cominciare con i seminari. Grazie a tutti! [1] https://doodle.com/poll/k4z8py3hwp3gen74 A presto, -- Leonardo.

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Annuncio seminario Prof. Rinaldi, 5 febbraio 11:30
by Federico Poloni 30 Jan '19

30 Jan '19

Inoltro questo annuncio di seminario a informatica. *Data*: Martedì 5 Febbraio, 11-30-12:30, Sala Gerace, Dipartimento di Informatica * * *Speaker*: Prof. Francesco Rinaldi, Università di Padova *Title*: Advances on first order algorithms for constrained optimization problems in Machine Learning *Abstract*: Thanks to the advent of the "Big Data era", simple iterative first-order optimization approaches for constrained optimization have re-gained popularity in the last few years. In the talk, we first review a few classic methods (i.e., conditional and projected gradient method) in the context of Big Data applications. Then, we discuss both theoretical and computational aspects of some variants of those classic methods. Finally, we examine current challenges and future research perspectives. *Ambito*: Progetto PRA 2017

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Annuncio di Seminario
by Leonardo Robol 17 Jan '19

17 Jan '19

Speaker: Daniel Kressner Affiliation: EPFL Time: Wednesday, 9 January 2019, h. 11:00 Place: Aula Seminari, Dipartimento di Matematica Title: Tensorized Krylov subspace methods: Algorithms, analysis, and applications Tensorized Krylov subspace methods are a versatile tool in numerical linear algebra for addressing large-scale applications that involve tensor product structure. This includes the discretization of high-dimensional PDEs, the solution of linear matrix equations, as well as low-rank updates and Frechet derivatives for matrix functions. This talk gives an overview of such methods, discusses their theoretical properties, and highlights applications.

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Annuncio di seminario
by Leonardo Robol 12 Dec '18

12 Dec '18

Buongiorno, allego l'annuncio del seminario per la settimana prossima, che sarà tenuto da Giulio Masetti (ISTI-CNR). Colgo l'occasione per ricordarvi l'appuntamento di domani, per il seminario di Stefano Massei, alle 10:00 in Aula Seminari Ovest, Informatica. -- Leonardo Robol. ==== Speaker: Giulio Masetti Affiliation: ISTI-CNR Time: Thursday, 13 December 2018, h. 10:00 Place: Aula Seminari, Dipartimento di Matematica Title: Computing dependability-oriented measures on Markov chains by means of matrix functions In the context of computing and communication system, dependability is defined as the ability to deliver service that can justifiably be trusted. Dependability is then an umbrella term that encompasses several attributes, such as: availability, reliability, safety, integrity, maintainability, and confidentiality. Design and analysis of models capable to express functional specifications and behavioural aspects is an important part of the system dependability justification process. In particular, Markov chains reflect important characteristics of computing systems such as discrete states and memoryless property, and then are often employed to model complex systems. Starting from the model Markovian process, other processes can be defined to express gains or losses according to which state the Markov process is in, and then all the mentioned dependability attributes can be evaluated as measures on these processes. More and more complex systems are designed, and then new techniques are required to tackle the evaluation of dependability-oriented measures on large models. In a world where systems comprise hundreds or thousands of interconnected components, justifying dependability is an ever increasing challenge. The main contribution presented in this talk is, focusing on Continuous Time Markov Chains, recasting dependability-oriented measures as the evaluation of a bilinear form where the matrix is indeed a matrix function of the infinitesimal generator matrix characterizing the Markovian stochastic process. In particular, chains with absorbing states, relevant to evaluate system reliability and connected attributes, represent one of the main challenges the modeling community has to deal with, and -- we think -- one of the cases where applying results from the matrix functions body of knowledge can have the greater impact.

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Annuncio di seminario
by Leonardo Robol 29 Nov '18

29 Nov '18

Buongiorno, allego l'annuncio del seminario per la settimana prossima, che sarà tenuto da Stefano Massei (EPF Lausanne). L'appuntamento è giovedì 6 dicembre alle 10:00 presso il Dipartimento di Informatica, Sala Seminari Ovest. -- Leonardo Robol. ==== Speaker: Stefano Massei Affiliation: EPF Lausanne Time: Thursday, 6 December 2018, h. 10:00 Place: Sala Seminari Ovest, Dipartimento di Informatica. Title: A low-rank technique for computing the quasi stationary distribution of Galton-Watson processes Branching processes describe the dynamics of a population of individuals which reproduce and die independently, according to some specific probability distributions. More precisely, we assume that any individual has a unit lifetime, at the end of which it might give birth to one or more offsprings simultaneously. This is encoded into the probability generating function P(z):=\sum p_j z^j where p_j is the probability of generating j individuals. These kind of processes are known in the literature as Galton-Watson processes. We consider populations that are certain to become extinct, yet appear to be stationary over any reasonable time scale. More precisely, we are interested in characterizing the quasi-stationary distribution of the process, i.e., the asymptotic distribution of the population size, conditional on its survival. Yaglom proved that if m:=P'(1)<1 then the quasi stationary distribution exists and its probability generating function G(z):=\sum g_j z^j solves the Schroeder functional equation G(P(z))= mG(z)+1-m, z in [0,1]. (*) We study the link between the regularity of P(z) and that of G(z) and we propose a strategy for solving (*) in the case where P(z) and G(z) are analytic on a disc of radius r>1. We see that the discretization of (*) leads to a numerical method that is capable to find arbitrary accurate approximations of the coefficients of G(z). Moreover, we point out the (numerical) low-rank structure that appears in the discretized problem, and we show how to exploit it in the proposed procedure.

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Annuncio di seminario
by Leonardo Robol 26 Nov '18

26 Nov '18

Buongiorno, allego l'annuncio del seminario di Marcus Carlsson, programmato per la prossima settimana. Il seminario si terrà in SNS, e sarà di martedì e non di giovedì. -- Leonardo Robol. ==== Speaker: Marcus Carlsson Affiliation: Lund University Time: Tuesday, 27 November 2018, h. 11:00 Place: Aula Bianchi scienze, SNS Title: Perturbation theory for the spectral decomposition of matrices Consider a Hermitian matrix and a small perturbation. We will consider how the eigenvalues and eigenvectors change with the perturbation. Typical theorems concerning this either consider a perturbation along a line or provide general estimates valid for all perturbations (such as Weyl’s inequalities). We first give an overview of the field and then provide new results which are global in the sense that the perturbation is not restricted to a line, but local in the sense that the estimates are valid modulo certain ordo terms. We apply this to the functional calculus of the matrix square root and matrix modulus. In the kernel-free case the corresponding result follows from the so called Daleskii-Krein theorem.

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Avviso di seminario (e reminder)
by Leonardo Robol 22 Nov '18

22 Nov '18

Buongiorno, allego l'annuncio del secondo seminario nella serie NumPI, e con l'occasione vi ricordo l'appuntamento di domani alle 10:00 per quello di Giovanni Barbarino (Sala Seminari Est, Dipartimento di Informatica). ==== Speaker: Jie Meng Affiliation: Pusan National University Time: Thursday, 22 November 2018, h. 10:00 Place: Sala Seminari, Dipartimento di Matematica, Università di Pisa Title: On the positive definite solution of the nonlinear matrix equation X^p=A+M^T(X#B)M The nonlinear matrix equation X^p = A + M^T (X # B)M is considered, where p ≥ 1 is a positive integer, M is an n × n nonsingular matrix, A is a positive semidefinite matrix and B is a positive definite matrix. We call C # D the geometric mean of positive definite matrices C and D. Some properties of the positive definite solution of the nonlinear matrix equation is investigated, including the existence and uniqueness of the solution, a lower and an upper bound. Iteration method for finding the numerical solution is proposed. Perturbation bounds with respect to small perturbations on the coefficient matrices are obtained. -- Leonardo Robol

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