Search

We study the perturbation bound for the spectral radius of an mth-order n-dimensional nonnegative tensor A. The main contribution of this paper is to show that whenAis perturbed to a nonnegative tensor à by ΔA, the absolute difference between the spectral radii of A and à is bounded by the largest magnitude of the ratio of the ith component of ΔAxm-1 and the ith component xm-1, where x is an eigenvector associated with the largest eigenvalue of A in magnitude and its entries are positive. We further derive the bound in terms of the entries of Aonly when x is not known in advance. Based on the perturbation analysis, wemake use of the NQZ algorithmto estimate the spectral radius of a nonnegative tensor in general. On the other hand, we study the backward errormatrix ΔA and obtain its smallest error bound for its perturbed largest eigenvalue and associated eigenvector of an irreducible nonnegative tensor. Based on the backward error analysis, we can estimate the stability of computation of the largest eigenvalue of an irreducible nonnegative tensor by the NQZ algorithm. Numerical examples are presented to illustrate the theoretical results of our perturbation analysis. [ABSTRACT FROM AUTHOR]