矩阵方程X+A~*X^(-n)A=I的正定解

A Positive Definite Solution for Matrix Equation X+A~*X^(-n)A=I

讨论了矩阵方程X+A*X-nA=I在A为正定矩阵和酉矩阵时的正定解的存在性、唯一性、误差估计及存在正定解的必要条件,并且构造了数值求解的迭代方法.

This paper discusses the existence, uniqueness, error estimation of positive definite solution and necessary condition for the existence of positive definite solution, while A being the positive definite matrix and unitary matrix in the matrix equation X＋A＊X^-nA=I. It also constructs the iterative method of numerical value solution.