关于矩阵方程X+A~*X^(-1)A=P的解及其扰动分析

ON THE MATRIX EQUATION X+ A~*X^(-1)A = P : SOLUTION AND PERTURBATION ANALYSIS

考虑非线性矩阵方程X+A~*X^(-1)A=P,其中A是n阶非奇异复矩阵,P是n阶Hermite正定矩阵.本文给出了Hermite正定解和最大解的存在性以及获得最大解的一阶扰动界,改进了文[5,6]中的部分结论.

The Hermitian positive definite solutions of the matrix equation X＋A^＊（X^-1）A=P are studied, where A is an n×n nonsingular matrix and P is an n×n Hermitian positive definite matrix. The existence of the Hermitian positive definite solutions is proved and the first order perturbation bound of the maximal solution is presented, which improves the corresponding partial results in [5,6].