SOLUTIONS AND PERTURBATION ESTIMATES FOR THE MATRIX EQUATION X+A~*X~(-n)A=P
矩阵方程X+A~*X~(-n)A=P的Hermite正定解及其扰动分析

The nonlinear matrix equation X+A~*X~(-n)A=P is studied,where A is an m×m nonsingular matrix and P is an m×m Hermite positive definite matrix.The existence of the Hermite positive definite solutions is studied and the properties of the maximal solution are discussed.Moreover,iteration algorithms for the maximal and the minimum solutions are offered.And by means of differential,two new first order perturbation bounds for the maximal solution are obtained.The results are illustrated by several numerical examples.