PERTURBATION ANALYSIS FOR THE MATRIX EQUATIONS X ± A∗X−1A = I

Abstract

The nonlinear matrix equations $X\pm A^{*}X^{-1}A=I$ are investigated, where $A$ is an $n\times n$ nonsingular matrix and $I$ is an $n\times n$ identity matrix. Some new perturbation bounds for Hermitian positive definite solutions of these equations are derived by using elementary calculus techniques developed in[Sun J G , BIT, 31(1991), pp.341-352] and [Barrlund A, BIT, 31(1991), pp.358-363]. The new results are illustrated by numerical examples.