Randomized error estimation for eigenvalue approximation

Abstract

This paper analyzes the randomized error in the sense for eigenvalue and eigenvector estimation by methods based on Krylov information. In particular, the randomized analysis of the power method presented in previous works [1, 2, 11] for real symmetric matrices is generalized to normal matrices. For positive definite matrices we give a randomized algorithm for computing the condition number and we study its randomized error. Moreover, we give upper bounds on the randomized error for estimating the smallest eigenpair by the Lanczos method.