May 2016 - NumPI - Mailing list — Dipartimento di Matematica, UniPI

Reminder: Optimization & Numerical Analysis seminars: Brugiapaglia
by Federico Poloni 20 Jun '16

20 Jun '16

Speaker: Simone Brugiapaglia Affiliation: Politecnico di Milano --- Laboratory for Modeling and Scientific Computing MOX Time: Tuesday, December 15, 11 am Place: Sala Seminari Est, Dipartimento di Informatica, Università di Pisa Title: CORSING: Sparse approximation of PDEs based on Compressed Sensing Abstract: We present a novel method for the numerical approximation of PDEs, motivated by recent developments in sparse representation, and particularly by compressed sensing. We named this approach CORSING (COmpRessed SolvING). Establishing an analogy between the sampling of a signal and the Petrov-Galerkin discretization of a PDE, the CORSING method can recover the best s-term approximation to the solution with respect to N suitable trial functions, with s<<N, by evaluating the bilinear form associated with the PDE against a randomized choice of m<<N test functions. This yields an underdetermined m x N linear system, that is solved by means of sparse optimization techniques. A theoretical analysis of the CORSING procedure is presented, based on the concepts of local a-coherence and restricted inf-sup property, along with numerical experiments that confirm the robustness and reliability of the proposed strategy. === Everyone is welcome! -- --federico poloni

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Fwd: cancellazione seminario
by Dario A. Bini 30 May '16

30 May '16

Mi dispiace dovere annunciare la cancellazione del seminario di Stefano Serra Capizzano previsto oggi alle 11:00. Purtroppo nel viaggio di rientro dagli USA, per un guasto all'aereo per Austin, Stefano ha perso la coincidenza da new York per Roma. Dario

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Avviso di Seminario
by Dario A. Bini 30 May '16

30 May '16

Speaker: Stefano Serra Capizzano, Universita' dell'Insubria Titolo: Spettri, Matrici e Applicazioni nella Approssimazione di Equazioni alle Derivate Parziali Abstract: La presentazione è volta ad illustrare come dedurre informazioni sullo spettro di matrici provenienti dalla approssimazione numerica di equazioni alle derivate parziali: il secondo passo, di interesse squisitamente numerico, consiste nell'impiegare l'informazione ottenuta per il 'design' di metodi efficienti per il calcolo della soluzione dei risultanti sistemi lineari di grandi dimensioni. La chiacchierata, molto informale, includerà una breve discussione su alcuni problemi applicativi. Data: 30 Maggio 2016, ore 11:00 Luogo: Sala riunioni, Dipartimento di Matematica

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Fwd: [Dipartimento.di] Mauriana Pesaresi Seminar Update
by Federico Poloni 11 May '16

11 May '16

Scusate il nuovo messaggio ma c'è un cambio di location per il seminario che vi ho appena inoltrato. -f -------- Forwarded Message -------- Subject: [Dipartimento.di] Mauriana Pesaresi Seminar Update Date: Wed, 11 May 2016 17:34:43 +0200 From: Marco Grandi <marco.grandi(a)di.unipi.it> To: dipartimento(a)di.unipi.it Dear all, the location of tomorrow's Mauriana Pesaresi Seminar has been changed from East Seminar Room to Open Lab. Below updated information on the seminars. Speaker: Giulio Masetti Date: 12 May 2016, 13:00 Place: Open Lab (Room 306) Marco Grandi ______________________________________________ Dipartimento.di mailing list Dipartimento.di(a)listgateway.unipi.it http://listgateway.unipi.it/mailman/listinfo/dipartimento.di

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Fwd: [Dipartimento.di] Mauriana Pesaresi Seminar
by Federico Poloni 11 May '16

11 May '16

Inoltro questo avviso di seminario che sembra di argomento interessante per gli iscritti alla lista. -federico -------- Forwarded Message -------- Subject: [Dipartimento.di] Mauriana Pesaresi Seminar Date: Wed, 11 May 2016 10:53:01 +0200 From: Francesca Pratesi <pratesi(a)di.unipi.it> Organization: University of Pisa To: dottorandi(a)di.unipi.it, dipartimento(a)di.unipi.it Dear all, I would like to remind you that the next Mauriana Pesaresi Seminar will be held tomorrow, 12 May. Below further information on the seminars. Title2: Impact of Equations Ordering on Inexact and Quasi-Inverse Newton Methods. Speaker2: Giulio Masetti Date2: 12 May 2016, 13:00 Place2: East Seminar Room Abstract2: The Newton-Raphson method has a prominent role in applied science and engineering. Our research group at SEDC lab., ISTI/CNR, is involved in dependability-related assessment of Smart Electrical Grids and the Newton-Raphson method is used to solve numerically the system of power-flow equations that characterize the electrical network. In general, given a system of non-linear equations written in the form F(u)=0, where F is a continuously differentiable function that maps a n-dimensional vector u to a n-dimensional vector F(u), one of the solutions can be found via the Newton-Raphson method. At each iteration of this method, a linear system that involves the Jacobian matrix J_{F}(u) of F has to be solved and the equation ordering does not affect it. At increasing the size of the problem, solving with a direct method the linear system is often impractical (w.r.t. time and space complexity, and accuracy), even if the Jacobian is a sparse matrix. Therefore, in these cases iterative methods have been studied, where, the equation ordering becomes a critical aspect to analyse carefully. Studies related to equations ordering are available on techniques employed in medium-size linear systems, such as the Gauss-Seidel method. In this method, at each iteration, permutations of Jacobian rows and columns, that do not depend on the initial equation ordering, are exploited to gain in CPU time. Jacobian-free techniques, developed to solve very large linear problems, offer interesting opportunities for investigations on the impact of initial equations ordering over the number of iterations. One of the most effective algorithms in this category is the Inexact-Newton-Krylov: it gets rid of the Jacobian matrix and approximates the matrix-vector product J_{F}(u)v with the finite difference [F(u+sv)-F(u)]/s. Another variant of Newton- Raphson is the Quasi-Inverse-Newton: it approximates the inverse of the Jacobian J_{F}^{-1}(u) with a diagonal matrix and solves directly the linear system. A seminal article, written by L. Dutto and published on the International Journal for Numerical Methods in Engineering in 1993, numerically presents the influence of initial ordering over the preconditioner of Inexact- Newton-Krylov GMRES, and then on the number of iterations. However, it does not address the impact of ordering on the core of the method, that is the adopted Jacobian-free techniques. To go further such existing results, our study focuses on Jacobian- free methods and explores the influence of the initial ordering over them. In this talk, we discuss our approach to prove that the initial equations ordering affects Inexact-Newton-Krylov and Quasi- Inverse-Newton, also presenting a preliminary analysis to quantify the resulting impact. A trivial bivariate function will be used as case study and numerical experiments will be presented. Interestingly, the equations ordering does not only affect the efficiency in reaching a solution, but also the solution itself. As next step, we are working on exploring more realistic scenarios in the power grid domain. Traditionally, the characteristics of the domain at hand has influenced the application of mathematical structures. For example, when using Gauss-Seidel in the power-flow context, there exists a particular initial ordering such that the Jacobian is a four-block matrix and each block corresponds to well defined electrical quantities. Using Jacobian-free methods the application-oriented initial equations ordering could not be the best choice with respect to iterations number and reachable solutions. We believe this is an important feature, that the user of these methods need to be aware of. -- Francesca Pratesi Ph.D. Student - University of Pisa Room 296a - Phone 050 2212731 Department of Computer Science, Largo B. Pontecorvo 3, 56127 Pisa ______________________________________________ Dipartimento.di mailing list Dipartimento.di(a)listgateway.unipi.it http://listgateway.unipi.it/mailman/listinfo/dipartimento.di

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Funerali
by Francesco Romani 09 May '16

09 May '16

Il funerali della madre di Grazia Lotti sono domani alle 11 alla cappella del cimitero della Misericordia. Francesco. ____________________________ Prof. Francesco Romani Dipartimento di Informatica Via Buonarroti 2, 56127 PISA, ITALY Tel +39-050-2212734 FAX +39-050-2212726 http://www.di.unipi.it/~romani

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