NumPI May 2017

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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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NumPI May 2017