Sylvester矩阵方程的改进IO迭代算法  

IMPROVED IO ITERATIVE ALGORITHM FOR SYLVESTER MATRIX EQUATION

作　　者：康靖 马昌凤[1] KANG Jing;MA Chang-feng(School of Mathematics and Statistics,Fujian Normal University,Fuzhou,Fujian 350007,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117

出　　处：《井冈山大学学报（自然科学版）》2023年第2期1-8,共8页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(11901098);福建省自然科学基金项目(2020J05034).

摘　　要：通过对Sylvester矩阵方程的理论分析,可知IO迭代算法中迭代矩阵的谱半径随内迭代次数的增大而减小,更新了IO迭代算法中内迭代次数的选择方法,并证明了该算法收敛性与初始矩阵无关。Sylvester矩阵在满足一些特定条件下,为了进一步提高收敛速度,可通过选择适当的相关参数,使得IO迭代算法有较好的收敛速度且比Smith算法的迭代次数明显减少。Through the theoretical analysis of the Sylvester matrix equation,it is known that the spectral radius of the iterative matrix in the IO iteration algorithm decreases with the increase of the number of inner iterations.The selection method of the number of inner iterations in the IO iteration algorithm is updated,and the convergence of the algorithm is proved to be independent of the initial matrix.When the Sylvester matrix satisfies some specific conditions,in order to further improve the convergence speed,by selecting appropriate relevant parameters,the IO iteration algorithm has a better convergence speed and the number of iterations is significantly reduced than that of the Smith algorithm.

关 键 词：Sylvester矩阵方程 IO迭代算法 Smith算法 收敛性 迭代因子 

分 类 号：O224.2[理学—运筹学与控制论]