摘要
本文讨论了非线性矩阵方程X-A*X-pA=Q在p>1时正定解存在的必要条件和充分条件以及正定解的一些性质,推导出此方程存在唯一正定解的充分条件,同时构造了数值求解的迭代方法,并且把某些已知的结论推广到任意实数p>1。
In this paper, we investigate the nonlinear matrix equation X - A^＊X^-pA = Q where p ：〉 1. We derive necessary conditions and sufficient conditions for the existence of positive definite solutions for the equation. We provide a sufficient condition for the equation to have a unique positive definite solution. We also propose an iterative method for finding positive definite solutions of the equation. Some of existing results are extended.
出处
《工程数学学报》
CSCD
北大核心
2009年第2期305-309,共5页
Chinese Journal of Engineering Mathematics
基金
山东省自然科学基金(Y2006A14)
山东大学威海分校青年成长基金
关键词
矩阵方程
正定解
迭代方法
matrix equation
positive definite solution
iterative method
