Perturbation Analysis for the Matrix Equation X − ∑ i = 1 m A i ∗ X A i + ∑ j = 1 n B j ∗ X B j = I

Abstract

We consider the perturbation analysis of the matrix equation $X-{\sum }_{i=1}^m{A}_i^{\ast }X{A}_i+{\sum }_{j=1}^n{B}_j^{\ast }X{B}_j=I$. Based on the matrix differentiation, we first give a precise perturbation boundfor the positive definite solution. A numerical example is presented to illustrate the sharpnessof the perturbation bound.