%0 Journal Article
%T SOLUTION AND PERTURBATION ESTIMATES FOR THE MATRIX EQUATION X-A*X-2A=Q<br>矩阵方程X-A*X-2A=Q的正定解及其扰动分析
%A Yin Xiaoyan Liu Sanyang Xiao Gang
%A <br>尹小艳
%A 刘三阳
%A 肖刚
%J 计算数学
%D 2009
%I 
%X 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.
%K nonlinear matrix equation
%K fixed point theorem
%K Hermitian positive definite solution
%K perturbation bound
%K condition number<br>非线性矩阵方程
%K 不动点定理
%K 正定解
%K 扰动界
%K 条件教
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=CC77F3CEF526D9CF0B3021650FB4E57E&aid=F26EDD3952B4EE9214B4495627FBC2A6&yid=DE12191FBD62783C&vid=4AD960B5AD2D111A&iid=0B39A22176CE99FB&sid=70AC2EF7F2065E09&eid=4C100B7696CE9E24&journal_id=0254-7791&journal_name=计算数学&referenced_num=0&reference_num=9