求一类分数逆幂矩阵方程对称解的Newton-BCR算法研究  

Newton-BCR Algorithm for Solving Symmetric Solutions of a Class of Fractional Inverse Power Matrix Equations

作　　者：吕长青 梁胜 LV Chang-qing;LIANG Sheng(School of Mathematics and Statistics,Zaozhuang University,Zaozhuang 277160,China)

机构地区：[1]枣庄学院数学与统计学院,山东枣庄277160

出　　处：《枣庄学院学报》2021年第5期53-64,共12页Journal of Zaozhuang University

基　　金：枣庄学院国家自然科学基金预研项目(项目编号:2019YY01);山东省本科教学改革面上项目(项目编号:M2020051).

摘　　要：含分数逆幂的单变量矩阵方程产生于控制论、控制系统、梯形网格、动态规划等领域,并在非线性博弈中有着重要的应用.首先,对含分数逆幂的单变量矩阵方程采用Newton算法进行求解.其次,针对在Newton迭代中导出的线性矩阵方程,给出了求其对称解的BCR算法,并对所提算法给出了收敛性证明.最后,通过数值实验验证所给算法的可行性和有效性.In this paper,the double iteration method for solving the symmetric solution of a class of univariate matrix equation with fractional inverse power has been investigated.Firstly,the Newton algorithm is used to solve the single variable matrix equation with fractional inverse power.In each iteration,a linear matrix equation about the correction matrix is derived.These linear matrix equations have the same structure,but the elements of the coefficient matrix and the constant matrix are different.Secondly,for the linear matrix equation,a BCR algorithm is given to find its constrained solution,and the convergence of the algorithm is proved.Finally,the feasibility and effectiveness of the algorithm are verified by numerical experiments.

关 键 词：分数逆幂 非线性矩阵方程 Newton算法 BCR算法 

分 类 号：O241.6[理学—计算数学]