Perturbation analysis of a quadratic matrix equation associated with an M-matrix

摘要

This paper is devoted to the perturbation analysis for the quadratic matrix equation X2−EX−F=0, where E is a diagonal matrix and F is an M-matrix. The quadratic matrix equation of this type arises in noisy Wiener–Hopf problems for Markov chains. The solution of practical interest is a particular M-matrix solution. In this paper the perturbation bound of the M-matrix solution is presented, meanwhile the residual bound for an approximate solution to the M-matrix solution is obtained. The theoretical results are illustrated by using simple numerical examples.