非线性矩阵方程X-A^(*)(R+B^(*)XB)^(-t)A=Q的正定解  

Positive definite solutions to nonlinear matrix equation X-A^(*)(R+B^(*)XB)^(-t)A=Q

作　　者：钟艳林[1] 孙德红[1] 李璞金 ZHONG Yanlin;SUN Dehong;LI Pujin(College of Information Engineering,Minnan University of Science and Technology,Quanzhou 362700,China;School of Mathematics and Com puter Science,Shanri Normal University,Taiyuan 03003l,China)

机构地区：[1]闽南理工学院信息工程学院,福建泉州362700 [2]山西师范大学数学与计算机科学学院,山西太原030031

出　　处：《延边大学学报(自然科学版)》2025年第1期1-5,共5页Journal of Yanbian University(Natural Science Edition)

基　　金：国家自然科学基金项目(12271318);福建省引导性项目(2024H0038).

摘　　要：利用闭凸集上单调算子不动点定理,给出了非线性矩阵方程X-A^(*)(R+B^(*)XB)^(-t)A=Q存在正定解的条件,并通过构造迭代矩阵序列的方法求得了非线性矩阵方程的正定解.利用数值算例进行验证表明,所给迭代矩阵序列方法是可行性的.This paper employs the monotone operator fixed-point theorem on closed convex sets to establish the conditions for the existence of positive definite solutions to nonlinear matrix equation X-A^(*)(R+B^(*)XB)^(-t)A=Q.By constructing a sequence of iterative matrices,the positive definite solutions to the nonlinear matrix equations are obtained.Numerical examples are utilized to verify the feasibility of the proposed iterative matrix method,demonstrating its feasibility.

关 键 词：非线性矩阵方程 正定解 迭代方法 不动点 

分 类 号：O246[理学—计算数学]