%0 Journal Article
%J Numerische Mathematik
%D 2003
%T On the powers of a matrix with perturbations
%A Stewart, G.W.
%X Let A be a matrix of order n. The properties of the powers A k of A have been extensively studied in the literature. This paper concerns the perturbed powers Pk=(A+Ek)(A+Ek−1)(A+E1) where the E k are perturbation matrices. We will treat three problems concerning the asymptotic behavior of the perturbed powers. First, determine conditions under which Pk0 . Second, determine the limiting structure of P k . Third, investigate the convergence of the power method with error: that is, given u 1 , determine the behavior of u k =ngr k P k u 1 , where ngr k is a suitable scaling factor.
%B Numerische Mathematik
%V 96
%P 363 - 376
%8 2003///
%G eng
%N 2
%R 10.1007/s00211-003-0470-0