广西民族大学学报（自然科学版）2025，Vol.31Issue(4)：77-83,7.
求解一类非线性矩阵方程正定解的无逆迭代算法
Inverse-free Iterative Algorithm for Solving Positive Definite Solutions of a Class of Nonlinear Matrix Equations
摘要
Abstract
This paper discuss an iterative method for Hermite positive definite solutions of the nonlinear matrix equation X+A*X-tA=I.Firstly,by using the coefficient matrix,the existence interval of a Hermite positive definite solution of the matrix equation is established,and a new inverse-free iterative scheme is proposed.The research idea of the new algorithm is constructed,and the convergence of the proposed iterative algorithm is then proved by utilizing a partial order and the monotonic boundedness of the iterative sequence.It is also shown that when the coefficient matrix A is normal,the generated iterative sequences{Xk}and{Yk}are commutative.Finally,three numerical examples demonstrate that the proposed method is superior to existing inverse-free iterative algorithms.关键词
非线性矩阵方程/Hermite正定解/无逆迭代/迭代序列/收敛性Key words
Nonlinear matrix equation/Hermite positive definite solution/Inverse-free/Iterative sequence/Convergence分类
数理科学引用本文复制引用
熊昊,王云,黄玉莲..求解一类非线性矩阵方程正定解的无逆迭代算法[J].广西民族大学学报（自然科学版）,2025,31(4):77-83,7.基金项目
江苏省研究生科研与实践创新项目(KYCX24_2671) （KYCX24_2671）
中国矿业大学研究生创新项目(2024WLKXJ112). （2024WLKXJ112）
