On the positive definite solutions of the matrix equations Xs±ATX−tA=In

The two matrix equations Xs+ATX−tA=In and Xs−ATX−tA=In are studied. Based on the fixed-point theory, the existence of the symmetric positive definite solutions are proved. Sensitivity analysis of the maximal solution is presented. Some elegant estimates of the positive definite solutions are obtained. Three iterative methods for computing the positive solutions are proposed.