矩阵方程X+A*X-1A+B*X-2B=I正定解的一种求解方法  

A Solving Method of Positive Definite Solution about the Equation X+A*X-1A+B*X-2B=I

作　　者：刘丽波[1] 崔晓梅[1] LIU Libo;CUI Xiaomei(College of Sciences Jilin Institute of Chemical Technology,Jilin 132022,China)

机构地区：[1]吉林化工学院理学院

出　　处：《吉林化工学院学报》2019年第9期73-75,共3页Journal of Jilin Institute of Chemical Technology

摘　　要：主要给出了矩阵方程X+A^*X^-1A+B^*X^-2B=I的正定解的一种求解方法,即Hermite正定解.首先给出一个矩阵迭代序列;然后根据不动点理论给出了方程正定解存在的一个充分条件;最后通过给出一个具体的数值算例来说明本文方法的可行性.In this paper,we study the positive definite solution of a class matrix equations,that is the Hermite positive definite solution of the equation X+A^*X^-1A+B^*X^-2B=I.First,we show a matrix iterative sequence,then,according to the fixed point theory,a sufficient condition for the existence of positive definite solutions is given.Finally,numerical examples show the feasibility of the proposed method.

关 键 词：矩阵方程 迭代序列 正定解 正定矩阵 半正定矩阵 

分 类 号：O151.21[理学—数学]