Perturbation analysis of the maximal solution of the matrix equation X+A*X−1A=P. II Original Research Article

Consider the nonlinear matrix equationimageX+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 sharper perturbation bound for the maximal solution to the matrix equation is derived, explicit expressions of the condition number for the maximal solution are obtained, and the backward error of an approximate solution to the maximal solution is evaluated by using the techniques developed in [Linear Algebra Appl. 259 (1997) 183; Linear Algebra Appl. 350 (2002) 237]. The results are illustrated by using numerical examples.