非线性矩阵方程X^m-A＊X^-sA-B＊X^-tB=Q的Hermitian正定解  

The Hermitian positive definite solutions of the nonlinear matrix equation X^m-A*X^(-s)A-B*X^(-t)B=Q

作　　者：马昌凤[1] 柯艺芬[1] 

机构地区：[1]福建师范大学数学与计算机科学学院,福建省分析数学及其应用重点实验室,福建福州350117

出　　处：《邵阳学院学报（自然科学版）》2016年第3期5-9,共5页Journal of Shaoyang University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11071041);福建省自然科学基金项目(2016J01005)

摘　　要：研究了非线性矩阵方程X^m-A*X^(-s)A-B*X^(-t)B=Q的Hermitian正定解,其中Q为Hermitian正定矩阵,m∈[1,+∞)且s,t∈(0,1]。给出了该矩阵方程Hermitian正定解存在的充分必要条件,同时也分析了求解其Hermitian正定解的迭代算法的收敛性。实验结果表明了该迭代算法的有效性。In this paper,the Hermitian positive definite solutions of the nonlinear matrix equation X^m-A＊X^-sA-B＊X^-tB=Q are studied,where Q is a Hermitian positive definite matrix,m∈[1,＋∞） and s,t∈（ 0,1].The necessary and sufficient conditions for the existence of the Hermitian positive definite solutions are derived and the convergence of the proposed iteration method is analyzed.Numerical results demonstrate the efficiency of the proposed iteration method.

关 键 词：矩阵方程 Hermitian正定解 迭代方法 收敛条件 

分 类 号：O241.7[理学—计算数学]