一类非线性矩阵方程组的Hermite正定解  

The Hermite positive definite solution of a system of nonlinear matrix equations

作　　者：熊昊 黄敬频[1] 黄玉莲 XIONG Hao;HUANG Jingpin;HUANG Yulian(School of Mathematics and Physics,Guangxi Minzu University,Nanning,Guangxi 530006,China;College of Science,Southwest Petroleum University,Chendu,Sichuan 610500,China)

机构地区：[1]广西民族大学数学与物理学院,广西南宁530006 [2]西南石油大学理学院,四川成都610500

出　　处：《内江师范学院学报》2023年第2期37-43,共7页Journal of Neijiang Normal University

基　　金：国家自然科学基金资助项目(11661011)。

摘　　要：研究了一类非线性矩阵方程组的Hermite正定解求解问题.证明了矩阵方程组Hermite正定解的存在性并给出取值范围,构造出求解矩阵方程组的迭代方法并利用单调有界定理证明其收敛性,然后对其Hermite正定解进行扰动分析并给出扰动上界.最后运用数值算例说明所给方法的有效性及可行性.The problem of solving the Hermite positive definite solution for the system of nonlinear matrix equations is studied.Firstly,the existence of the Hermite positive definite solution of the system of matrix equations is proven,and the range of values is given.An iterative method for solving the system of matrix equations is constructed,and its convergence is proved by the monotone bounded theorem.Furthermore,the perturbation analysis is discussed and the erturbation upper bound is derived.Finally,numerical examples are given to illustrate the effectiveness and feasibility of the proposed iterative method.

关 键 词：非线性矩阵方程组 HERMITE正定解 不动点迭代 误差估计 扰动分析 

分 类 号：O241.7[理学—计算数学]