PERTURBATION ANALYSIS OF A NONLINEAR MATRIX EQUATION

Abstract

Consider the nonlinear matrix equation $X + A^* X^{-2}A = I$, where $A$ is an $n \times n$ complex matrix, $I$ the identity matrix and $A^*$ the conjugate transpose of the matrix $A$. In this paper a perturbation bound for a class of special solutions of this matrix equation is derived, and an explicit expression of its condition number is obtained. The results are illustrated by using some numerical examples.