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269 discussions

assegno di ricerca UNIPI
by Federico Poloni 21 Nov '17

21 Nov '17

Luca Gemignani mi comunica che è stato pubblicato il seguente bando per un assegno di ricerca sul progetto "Modelli e algoritmi innovativi per problemi strutturati e sparsi di grandi dimensioni" (scadenza domande 20 dicembre; necessario avere il dottorato). Info su https://www.unipi.it/ateneo/bandi/assegni/pra2017/inf/20dic2017/index.htm Un saluto a tutti, -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Seminar
by Dario Bini 02 Nov '17

02 Nov '17

Avviso di seminario: Speaker: Samandar Babaev (Bukhara State University, Uzbekistan) Date: Wednesday, November 8 Time: 11:00 Place: Sala Seminari, Dipartimento di Matematica Title: Optimal Interpolation Formulas in W_2^{(m,m-1)} space Abstract: In this talk, using S.L.Sobolev’s method, optimal interpolation formulas are constructed in /W_{2} ^/(/m,m//−/1)(0/,/1) space. Explicit formulas for coefficients of optimal interpolation formulas are obtained. Some numerical results are presented.

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Avviso di Seminario
by Dario Bini 26 Oct '17

26 Oct '17

Avviso di seminario: Speaker: Federico Poloni (Università di Pisa) Date: Tuesday 2017-10-31 Time: 11:00 Place: Sala Seminari Ovest, Dipartimento di Informatica Title: Counting Fiedler pencils using diagrams Fiedler pencils are a family of matrix pencils which generalizes the well-known companion matrix: they are*linearizations*, i.e., they provide a method to construct, given a matrix polynomial, a linear eigenvalue problem with the same eigenvalues and multiplicities. Fiedler pencils are constructed as products of special block matrices that act nontrivially only on two contiguous blocks. They have a rich structure that give rise to many combinatorial properties. In this talk, we introduce a notation that associates to each pencil a diagram that depicts its action on the blocks. Using this notation, we can obtain visual proofs of several statements in the theory, and we can solve several counting properties (such as "how many distinct Fiedler pencils with repetitions of a given dimension exist"). Among them, in particular, we are interested in counting Fiedler pencils associated to symmetric and palindromic matrix polynomials which preserve the same structure. This talk is based on a joint work with Gianna Del Corso.

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Avviso di seminario
by Dario A. Bini 13 Oct '17

13 Oct '17

Invio il seguente avviso di seminario Dario --- Gorno: Martedi 17 ottobre Ora: 11:00 Aula: Seminari, Dipartimento di Matematica Speaker: Leonardo Robol, ISTI --- CNR Titolo: Backward error analysis for polynomial rootfinders. Abstract: The most common methods to compute roots of polynomials is to rephrase the problem in linear algebra terms: one constructs a companion matrix (or pencil) that has the roots of the polynomial as eigenvalues. However, even when the eigenvalue method used is backward stable, it's non-trivial to map the backward error back on the polynomial. This problem has been studied extensively in the past and it has been shown that relying on the QR method does not provide a normwise backward-stable rootfinder. For this reason, one needs to rely on QZ + appropriate scaling. However, companion matrices are unitary plus rank 1, and we claim that relying on fast QR method that exploits this structure can lead to a backward-stable method. To this end, one needs to ensure that the errors on the unitary and rank 1 parts satisfy different bounds. We show how to perform this analysis of "mixed perturbation backward-error", as well as a method that satisfies these constrains. Time permitting, we discuss some more details that one should consider. We show, for example, that normwise backward stable operations (i.e., unitary rotations in our case) do not necessarily imply backward stable operations on the unitary and low-rank factors, unless some particular identities involving sines and cosines are preserved. This is joint work with Jared Aurentz, Thomas Mach, Raf Vandebril, and David Watkins.

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Optimization & Numerical Analysis seminars: Iannazzo
by Federico Poloni 26 Jul '17

26 Jul '17

Speaker: Bruno Iannazzo Affiliation: Università di Perugia, Italy Time: Thursday 2017-08-27, h. 11:00 Place: Sala Seminari Est, Dipartimento di Informatica, Università di Pisa Title: The Riemannian Barzilai-Borwein algorithm and the matrix geometric mean computation Abstract: We consider the problem of computing the geometric mean of positive definite matrices, the so-called Karcher mean. For this purpose, we adapt the Barzilai-Borwein method from nonlinear optimization to Riemannian manifold optimization. Incomporating a nonmonotone line-search strategy yields global convergence under standard assumptions, fulfilled in the problem of the matrix geometric mean. By a set of numerical tests, we show that the Riemannian Barzilai-Borwein method notably outperforms existing first-order optimization methods for computing the matrix geometric mean. === Everyone is welcome. Sorry for the short notice! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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Avviso di Seminario
by Dario A. Bini 11 Jul '17

11 Jul '17

Avviso di Seminario: Speaker: Rajendra Bhatia Affiliation: Indian Statistical Institute, Delhi Date: July 11 Time: 11:00 -- 12:00 Place: Aula Magna Title: The Bures-Wasserstein distance on positive definite matrices Abstract: We will discuss an interesting metric on the space of positive definite matrices, called the Bures distance in the quantum information literature and the Wasserstein metric in optimal transport. This has connections with Riemannian geometry, statistics, QIT and optimal transport. We will explain these connections. The two-variable and several-variable mean with respect to this metric will be described. Our perspective from matrix analysis leads to simpler proofs and suggests new problems.

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Seminari Benzi e Qi
by Federico Poloni 05 Jun '17

05 Jun '17

Buongiorno, segnalo questo seminario di Michele Benzi in SNS, e ne approfitto per ricordare anche quello di Liqun Qi di lunedì prossimo: > Speaker: Liqun Qi, The Hong Kong Polytechnic University, Department of > Applied Mathematics > > Title: Tensor Analysis: Spectral Theory and Special Tensors > > Room: Sala Riunioni, Dipartimento di Matematica > > Time: Monday, June 12, 11:00 -------- Forwarded Message -------- Subject: [Settimanale] avviso Seminario di Matematica prof. Michele Benzi (8.06.2017) Date: Mon, 5 Jun 2017 10:13:39 +0200 From: Valeria Giuliani <valeria.giuliani(a)sns.it> SEMINARIO DI MATEMATICA Giovedì 8 giugno 2017 ore 11:00 _Scuola Normale Superiore_ Pisa Aula Marie Curie *_ _* * **Michele Benzi*** /(Samuel Candler Dobbs Professor - Emory University)/ */ /* terrà un seminario dal titolo: *“**Decay properties of matrix functions with applications to electronic structure computations**”*** * * *Abstract:* /Functions of matrices, such as the matrix exponential or the square root, arise in a number of scientific and technical applications, ranging from quantum mechanical computations to the structural analysis of complex graphs and networks. The actual numerical evaluation of functions of large and sparse matrices can be quite challenging, and much effort has been devoted to this problem in recent years. An important property that is frequently exhibited by analytic functions of large and sparse matrices is the rapid off-diagonal decay of the matrix entries; careful exploitation of this property can lead to algorithms with optimal computational complexity (this means that the cost scales linearly with the dimension of the problem)./// /In this talk I will present some rigorous estimates on the size of the off-diagonal entries of analytic matrix functions. As a special case, the theory yields a proof of the exponential decay, or "localization", of the density matrix (spectral projector) arising in electronic structure computations for gapped systems, a classical problem in solid state physics and quantum chemistry. In addition to giving a precise mathematical form to W. Kohn's notion of "nearsightedness of electronic matter", these estimates provide a sound basis for the development of linear scaling methods./*//* */ /* Tutti gli interessati sono invitati a partecipare. Classe di Scienze Matematiche e Naturali Valeria Giuliani Scuola Normale Superiore Servizio alla Didattica e Allievi tel. 050 509260 Piazza dei Cavalieri, 7 56126 Pisa E-mail: valeria.giuliani(a)sns.it <mailto:valeria.giuliani@sns.it> E-mail: classi(a)sns.it <mailto:classi@sns.it>

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Fwd: ONE DAY ON NUMERICAL LINEAR ALGEBRA
by Federico Poloni 24 May '17

24 May '17

Ricevo da Dario Bini e inoltro. --- ONE DAY ON NUMERICAL LINEAR ALGEBRA June 14, 2017, Room 2AB40 - Dipartimento di Matematica "Tullio Levi-Civita", Universita' di Padova -Torre Archimede, Via Trieste 63, Padova Nel mese di giugno il Dipartimento di Matematica ospitera' tre reputati ricercatori internazionali nell'ambito dell'Algebra Lineare Numerica, di cui due vincitori delle selezioni Visiting Professor Cariparo 2016 e Visiting Scientist dell'Università di Padova. Si è dunque pensato di raccogliere i loro tre seminari in una giornata dedicata a tali tematiche. I seminari sono: 9:30-10:30 Gérard MEURANT (Paris, France) An optimal Q-OR method for solving nonsymmetric linear systems 11:00-12:00 Claude BREZINSKI (Univ. of Lille, France) Shanks sequence transformations and Anderson acceleration 14:30-15:30 Lothar REICHEL (Kent State University, USA) Generalized Krylov subspace methods for lp-lq minimization with application to image restoration Nella locandina allegata si puo' prendere visione degli abstracts e delle tempistiche di svolgimento dell'evento. La giornata si concludera' con una sessione di commenti e di discussione tra i partecipanti e gli speakers. Potranno pertanto essere sottoposti problemi particolari e richieste di approfondimenti. Tutti gli interessati sono invitati a partecipare. Non è prevista una registrazione, ma per ragioni logistiche, seppure non obbligatoria, sara' utile una potenziale manifestazione di partecipazione inviando una mail a michela(a)math.unipd.it Gli organizzatori M. Redivo-Zaglia, F. Tudisco

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Numerical analysis seminar: L.Q. Qi
by Federico Poloni 11 May '17

11 May '17

Speaker: Liqun Qi, The Hong Kong Polytechnic University, Department of Applied Mathematics Title: Tensor Analysis: Spectral Theory and Special Tensors Room: Sala Riunioni, Dipartimento di Matematica Time: Monday, June 12, 11:00 Abstract: Eigenvalues for tensors were introduced in 2005. Since then, a rich theory on eigenvalues of tensors and special tensors has been developed. There are two main definitions of eigenvalues of tensors. One definition is based upon homogeneous polynomial systems. This definition extends the definition of eigenvalues of matrices. A complex number is an eigenvalue of a ``square'' tensor if and only if it is a root of the characteristic polynomial of that tensor. The sum of all the eigenvalues of that tensor is equal to the sum of the diagonal entries of that tensor, while the product of all the eigenvalues of that tensor is equal to the determinant of that tensor. An eigenvalue of a real tensor with a real eigenvector is called an H-eigenvalue. An even order real symmetric tensor is positive semi-definite if and only if all of its H-eigenvalues are nonnegative. Various tensor eigenvalue inclusion theorems have been developed. Another tensor eigenvalue definition has the merit that the eigenvalues under this definition are invariant under orthonormal transformations. This makes eigenvalues under this definition found their applications in engineering, physics and mechanics. Based upon the tensor eigenvalue theory, theories on special tensors have also been developed. In particular, the Perron-Frobenius theory for irreducible nonnegative tensors and weakly irreducible nonnegative tensors has been developed, and found applications in spectral hypergraph theory and higher order Markov chains. Other special tensors include positive semi-definite tensors, sum-of-squares tensors, completely positive tensors and copositive tensors, etc. Eigenvalues of tensors also found their applications in magnetic resonance imaging, elastic mechanics, liquid crystal study, quantum entanglement and classicality problems, etc. A book “Tensor Analysis: Spectral Theory and Special Tensors'' is published by SIAM in April this year. ==== 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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Numerical Analysis Seminar: R. Vandebril
by Federico Poloni 04 Apr '17

04 Apr '17

Giorno: Lunedi' 10 Aprile Ora: 11:00 Luogo: Aula Seminari, Dip.to di Matematica Speaker: Raf Vandebril, KU Leuven Titolo: Eigenvalues and eigenvectors of matrix polynomials === 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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