矩阵方程X-A*X^(-2)A=Q的正定解及其扰动分析  

SOLUTION AND PERTURBATION ESTIMATES FOR THE MATRIX EQUATION X-A*X^(-2)A=Q

作　　者：尹小艳[1] 刘三阳[1] 肖刚[1] 

机构地区：[1]西安电子科技大学理学院,西安710071

出　　处：《计算数学》2009年第2期151-158,共8页Mathematica Numerica Sinica

基　　金：国家自然科学基金资助项目(60574075).

摘　　要：研究非线性矩阵方程X-A~*X^(-2)A=Q(Q>0)的Hermite正定解及其扰动问题.给出了该方程存在唯一Hermite正定解的充分条件及解的迭代计算公式.在此条件下,给出了该唯一解的扰动界及正定解条件数的一种表达式,并用数值例子对所得结果进行了说明.Consider the nonlinear matrix equation X-A^＊X^-2A=Q, where Q is Hermitian positive definite. It is proved that the matrix equation has a unique Hermitian positive definite solution provided α：= 2‖A‖2^2‖Q^-1‖2^3〈1, and under this condition, a perturbation bound for the Hermitian positive definite solution is derived. Moreover, an explicit expression of the condition number for the Hermitian positive definite solution is offered. The results are illustrated by some numerical examples.

关 键 词：非线性矩阵方程 不动点定理 正定解 扰动界 条件数 

分 类 号：O151.21[理学—数学] TP271.8[理学—基础数学]