Mike Shub

Universidad de Nueva York

Estados Unidos


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.

Marzo 2016

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