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Eigenvalues and Eigenvectors: Numerics, Dynamics, Complexity

Ponente: Michael Shub
Institución: Universidad de la Ciudad de Nueva York
Tipo de Evento: Investigación
Cuándo 09/03/2016
de 13:00 a 14:00
Dónde Auditorio "Alfonso Nápoles Gándara"
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Given an n by n real or complex matrix M, find one or all the pairs (eigenvalue, eigenvector) of M.  The problem is simple and pervasive, yet  there is no known (at least by me) numerical algorithm which has a simple list of desired features: a) stability , b) convergence with probability one and c) average polynomial complexity. I will survey some of the problems concerning  elimination theory and dynamical systems which arise. Finally I will present an algorithm satisfying all three criteria in the complex case.