Perturbation Analysis for the Matrix EquationX−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I

Abstract

We consider the perturbation analysis of the matrix equationX−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I. Based on the matrix differentiation, we first give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the sharpness of the perturbation bound.