On the perturbation estimates of the maximal solution for the matrix equation X+ATX−1A=P

In this paper we investigate the nonlinear matrix equation X+ATX−1A=P, for the existence of positive definite solutions. Bounds for ∥XL−1∥ and ∥X−1∥ are derived where XL is the maximal solution and X is any other positive definite solution of this matrix equation. A perturbation estimate for the maximal solution and an error bound for approximate solutions are derived. A numerical example is given to illustrate the reliability of the obtained results.