一类非线性矩阵方程的Hermite正定解  

On Hermitian Positive Definite Solutions of a Type of Nonlinear Matrix Equations

作　　者：尹小艳[1] 刘三阳[1] 房亮[1] 

机构地区：[1]西安电子科技大学应用数学系,西安710071

出　　处：《工程数学学报》2008年第4期597-604,共8页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(60574075)

摘　　要：本文讨论非线性矩阵方程Xs+A*X-tA=Q的Hermite正定解。利用不动点定理,研究了其正定解的存在性及包含区间;运用Banach压缩映像原理,建立了求极大解的迭代方法;最后给出数值例子对以上结果进行了说明。The Hermitian positive definite solutions of the nonlinear matrix equation X^S＋A^＊X^-tA=Q are studied. By using the Brouwer fixed-point theorem, a sufficient condition for the existence of the solutions is established. And using the Banach＇s fixed-point theorem, an iterative method for finding the maximal solution is given. Numerical experiments are offered to illustrate the results.

关 键 词：矩阵方程 正定解 迭代方法 BANACH压缩映象原理 范数 

分 类 号：O241.7[理学—计算数学]