摘要
研究矩阵方程X-A*X-αA-B*X-βB=I在α,β∈(0,1]时的正定解,给出了该方程有正定解的充要条件,得到了方程有唯一正定解的必要条件及求该解的迭代方法,并给出了求解该方程的两种迭代公式.
The positive definite solutions of the matrix equation X-A＊X-αA-B＊X-βB=I,α,β∈（0,1] were investigated.Necessary and sufficient conditions for the existence of positive definite solutions were derived,which generalize the existing related results.A necessary condition for the existence of the equation to have only a solution and the iterative formula for this solution were obtained.Finally,we got an inverse iterative method for solving the equation.
出处
《吉林大学学报（理学版）》
CAS
CSCD
北大核心
2010年第1期26-32,共7页
Journal of Jilin University:Science Edition
基金
吉林省教育厅"十一五"科学技术研究项目(批准号:吉教科合字[2008]第135号)
关键词
矩阵方程
正定解
迭代方法
matrix equation
positive definite solution
iterative method
