NumPI March 2016

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2 participants
5 discussions

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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Optimization & Numerical Analysis seminars: Sergeyev
by Federico Poloni 30 Mar '16

30 Mar '16

Speaker: Raf Vandebril Affiliation: KU Leuven Time: Thursday, April 7, h. 10:00 Place: Sala Seminari Ovest, Dipartimento di Informatica, Università di Pisa Title: A framework for structured linearizations of matrix polynomials in various bases Abstract: We present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described by the associated recurrence relations. The framework provides an extension of the classical linearization theory for polynomials expressed in non-monomial bases and allows to represent polynomials expressed in product families, that is, as a linear combination of elements of the form $\phi_i(x) \psi_j(x)$, where $\{ \phi_i(x) \}$ and $\{ \psi_j(x) \}$ can either be polynomial bases or polynomial families which satisfy some mild assumptions. We show that this general construction can be used for many different purposes. Among them, we show how to linearize sums of polynomials and rational functions expressed in different bases. As an example, this allows to look for intersections of functions interpolated on different nodes without converting them to the same basis. === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Optimization & Numerical Analysis seminars: Sergeyev (II)
by Federico Poloni 24 Mar '16

24 Mar '16

Speaker: Yaroslav D. Sergeyev Affiliation: Università della Calabria and N.I. Lobachevsky University of Nizhni Novgorod, Russia. Time: Tuesday, 12 April 2016, 12:00 Place: Sala Seminari Ovest, Dipartimento di Informatica, Università di Pisa Title: The Infinity Computer and numerical computations with infinities and in infinitesimals Abstract: The lecture presents a recent methodology allowing one to execute numerical computations with finite, infinite, and infinitesimal numbers on a new type of a computer – the Infinity Computer – patented in EU, USA, and Russia (see [23]). The new approach is based on the principle ‘The whole is greater than the part’ (Euclid’s Common Notion 5) that is applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a unique framework different from that of the non-standard analysis [...] http://pages.di.unipi.it/fpoloni/files/seminari/Sergeyev_Infinity.pdf === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Optimization & Numerical Analysis seminars: Sergeyev
by Federico Poloni 17 Mar '16

17 Mar '16

Speaker: Yaroslav D. Sergeyev Affiliation: Università della Calabria and N.I. Lobachevsky University of Nizhni Novgorod, Russia. Time: Monday, 11 April 2016, 15:00 Place: Sala Seminari Ovest, Dipartimento di Informatica, Università di Pisa Title: Lipschitz global optimization Abstract: Global optimization is a thriving branch of applied mathematics and an extensive literature is dedicated to it (see e.g., [1–24]). In this lecture, the global optimization problem of a multidimensional function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. It is supposed that the objective function can be “black box”, multiextremal, and non-differentiable. It is also assumed that evaluation of the objective function at a point is a time-consuming operation. Many algorithms for solving this problem have been discussed in literature. They can be distinguished, for example, by the way of obtaining information about the Lipschitz constant and by the strategy of exploration of the search domain. Different exploration techniques based on various adaptive partition strategies are analyzed. [...] http://pages.di.unipi.it/fpoloni/files/seminari/Sergeyev.pdf === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Seminari su Mathematica
by Francesco Romani 02 Mar '16

02 Mar '16

Nell’ambito del corso di Esperienze di programmazione saranno tenuti 4 seminari introduttivi di circa 2 ore sul linguaggio Mathematica. Mercoledì 9/3 11-13 Aula C1 Introduzione a Mathematica Mercoledì 16/3 11-13 Aula C1 Grafica con Mathematica Mercoledì 23/3 11-13 Aula C1 Programmazione in Mathematica Mercoledì 27/4 11-13 Aula C1 Calcolo Numerico con Mathematica La partecipazione è aperta a tutti e vi prego di diffondere l’informazione ad eventuali interessati. Grazie, saluti, FR ____________________________ 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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NumPI March 2016