矩阵方程X-A*X^(-q)A=Q当q>1时的Hermite正定解  

The Hermitian Positive Definite Solutions of Matrix Equation X - A*X^(-q)A = Q When q >1

作　　者：李静[1] 张玉海[1] 

机构地区：[1]山东大学数学与系统科学学院,济南250100

出　　处：《工程数学学报》2005年第4期679-686,共8页Chinese Journal of Engineering Mathematics

基　　金：数学天元基金(A0324654).

摘　　要：讨论了矩阵方程X-A*X-qA=Q在q>1时的Hermite正定解的存在性和解的性质,并且构造了两种数值求解的迭代方法。利用数值例子对以上结果进行了说明。We study the Hermitian positive definite solutions of the matrix equation X-A*X-qA = Q with q >1. Constructed are iterative methods for obtaining positive definite solutions of the equation. Sufficient conditions for the existence of positive definite solutions of the equation are given, and one property of the solutions is also discussed. The results are illustrated by numerical examples.

关 键 词：矩阵方程 正定解 迭代方法 

分 类 号：O241.7[理学—计算数学]