Numerische Mathematik

, Volume 96, Issue 2, pp 363–376

On the powers of a matrix with perturbations


DOI: 10.1007/s00211-003-0470-0

Cite this article as:
Stewart, G. Numer. Math. (2003) 96: 363. doi:10.1007/s00211-003-0470-0


Let A be a matrix of order n. The properties of the powers Ak of A have been extensively studied in the literature. This paper concerns the perturbed powers \({{ P_{{k}} = (A+E_{{k}})(A+E_{{k-1}})\cdots(A+E_{{1}}), }}\) where the Ek are perturbation matrices. We will treat three problems concerning the asymptotic behavior of the perturbed powers. First, determine conditions under which \({{P_{{k}}\rightarrow 0}}\). Second, determine the limiting structure of Pk. Third, investigate the convergence of the power method with error: that is, given u1, determine the behavior of ukkPku1, where νk is a suitable scaling factor.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of Computer Science and Institute for Advanced Computer StudiesUniversity of Maryland