矩阵方程AX+XB=C的对称解及其最佳逼近  

The Symmetric Solution of Matrix Equation and Its Optimal Approximation

作　　者：刘畔畔[1] 李庆春[1] 

机构地区：[1]北华大学数学学院,吉林吉林132013

出　　处：《江西师范大学学报（自然科学版）》2009年第1期17-21,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家"973"项目基金(2004CB318000)资助项目

摘　　要：提出一种求解线性矩阵方程AX+XB=C对称解的迭代法.该算法能够自动地判断解的情况,并在方程相容时得到方程的对称解,在方程不相容时得到方程的最小二乘对称解.对任意的初始矩阵,在没有舍入误差的情况下,经过有限步迭代得到问题的一个对称解.若取特殊的初始矩阵,则得到问题的极小范数对称解,从而巧妙地解决了对给定矩阵求最佳逼近解的问题.An iterative method to find the symmetric solution of the linear matrix equation AX ＋ XB = C is put forward in this paper. This iterative method can judgeautomatically the information of solutions. When the equation is consistent, it con-verges a symmetric solution of the equation. When the equation is inconsistent, it converges the least-squares symmetric solution of the equation. More over, for any initial matrix, a symmetric solution can be obtained within finite iteration steps in theabsence of roundoff errors. If a special kind of initial matrix is chosen, the syrnmetricsolution with least norm can be obtained, which wonderfully handle the problem of solving its optimal approximation solution for a given matrix.

关 键 词：线性矩阵方程 迭代法 对称解 最佳逼近解 最小二乘解 

分 类 号：O151.21[理学—数学]