Eigenvalues and Eigenvectors: Numerics, Dynamics, Complexity

Ponente: Michael Shub
Institución: Universidad de la Ciudad de Nueva York
Tipo de Evento: Researcher

When	Mar 09, 2016 from 01:00 PM to 02:00 PM
Where	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.