耦合矩阵方程的双对称最小二乘解及其最佳逼近  

The Least Squares Bisymmetric Solution Group of the Coupled Matrix Equation and Its Optimal Approximation

作　　者：刘莉[1] 王伟[1] 

机构地区：[1]宁夏大学数学计算机学院,银川750021

出　　处：《西南大学学报（自然科学版）》2014年第12期82-90,共9页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11201253)

摘　　要：由于用矩阵分解的方法求解耦合矩阵方程的双对称最小二乘解比较复杂,所以用迭代算法来求解该方程的双对称最小二乘解并证明了算法的收敛性,同时,极小范数解也可通过选取特殊的初始矩阵得到.利用此算法还可得到任意给定矩阵组的最佳逼近双对称解组.Owing to the difficulty of obtaining the bisymmetric solution of a coupled matrix equation by matrix decomposition ,an iterative method is proposed in this paper to solve the least squares bisymmetric solution group of the coupled matrix equation ,and its convergence is proved .Its least‐norm bisymmetric solution group can also be obtained by choosing the special kind of initial iterative matrices .In addition , the unique optimal approximation solution group to the given matrix group in Frobenius norm can be ob‐tained .

关 键 词：矩阵方程 双对称最小二乘解组 极小范数解组 最佳逼近解组 

分 类 号：O241.6[理学—计算数学]