Perturbation analysis of the maximal solution of the matrix equation X+A*X−1A=P

Consider the nonlinear matrix equation X+A*X−1A=P,where A, P are n×n complex matrices with P Hermitian positive definite, and A* denotes the conjugate transpose of a matrix A. In this paper a perturbation bound for the maximal solution of the matrix equation and a computable error bound for approximate solutions are derived by using an elegant property of the maximal solution. The results are illustrated by using numerical examples.