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

This paper is devoted to the perturbation analysis for the quadratic matrix equation X2−EX−F=0X2−EX−F=0, where EE is a diagonal matrix and FF is an MM-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 MM-matrix solution. In this paper the perturbation bound of the MM-matrix solution is presented, meanwhile the residual bound for an approximate solution to the MM-matrix solution is obtained. The theoretical results are illustrated by using simple numerical examples.