多变量矩阵方程的对称最小二乘解及其最佳逼近  

The least squares symmetric solutions of the matrix equation with several variables 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,宁夏银川750021

出　　处：《西北师范大学学报（自然科学版）》2014年第6期20-25,共6页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11201253)

摘　　要：鉴于用矩阵分解的方法求解多变量矩阵方程的复杂性,本文提出了一类迭代算法用于求解多变量矩阵方程的对称最小二乘解并证明了其收敛性,而且在选取特殊的初始对称矩阵组时,能得到它的极小范数解组.另外,给定任意矩阵组,利用此方法可得到它的最佳逼近对称解组.数值试验表明,这种方法相当有效.The least squares symmetric solutions of the matrix equation with several variables are too difficult to be obtained by applying matrices decomposition.An iterative method is presented to solve the least squares symmetric solutions of the linear matrix equation and its convergence is proved. And minimum norm of the least squares symmetric solutions can be obtained by choosing a special kind of initial symmetric matrices.In addition, the unique optimal approximation solutions to the given matrices in Frobenius norm can be obtained.The given numerical examples demonstrate that the iterative methods are quite efficient.

关 键 词：矩阵方程 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]