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矩阵方程X-A*X-2A=Q的正定解及其扰动分析
引用本文:尹小艳,刘三阳,肖刚.矩阵方程X-A*X-2A=Q的正定解及其扰动分析[J].计算数学,2009,31(2):151-158.
作者姓名:尹小艳  刘三阳  肖刚
作者单位:西安电子科技大学理学院,西安,710071
摘    要:研究非线性矩阵方程X-A*X-2A=Q(Q>0)的Hermite正定解及其扰动问题.给出了该方程存在唯-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.

关 键 词:非线性矩阵方程  不动点定理  正定解  扰动界  条件教
收稿时间:2007-07-17

SOLUTION AND PERTURBATION ESTIMATES FOR THE MATRIX EQUATION X-A*X-2A=Q
Yin Xiaoyan,Liu Sanyang,Xiao Gang.SOLUTION AND PERTURBATION ESTIMATES FOR THE MATRIX EQUATION X-A*X-2A=Q[J].Mathematica Numerica Sinica,2009,31(2):151-158.
Authors:Yin Xiaoyan  Liu Sanyang  Xiao Gang
Institution:Department of Mathematics;Xidian University;Xi'an 710071;China
Abstract: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 ositive definite solution provided a:=2||A||22||Q-1||23<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.  
Keywords:nonlinear matrix equation  fixed point theorem  Hermitian positive definite solution  perturbation bound  condition number  
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