矩阵方程AX+XB=C的双对称解及其最佳逼近  

The Bisymmetric Solution of Matrix Equation AX+XB=C 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：《大学数学》2011年第4期93-98,共6页College Mathematics

基　　金：国家"973"项目基金(2004CB318000)

摘　　要：提出一种求解线性矩阵方程AX+XB=C双对称解的迭代法.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双对称解,在方程不相容时得到方程的最小二乘双对称解.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双对称解.若取特殊的初始矩阵,则可以得到问题的极小范数双对称解,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 bisymmetric solution of the linear matrix equation AX＋XB=C is put forward in this paper.This iterative method can judge automatically the information of solutions.When the equation is consistent,it converges a bisymmetric solution of the equation.When the equation is inconsistent,It converges the least-squares bisymmetric solution of the equation.For any initial matrix,a bisymmetric solution can be obtained within finite iteration steps in the absence of roundoff errors.If a special kind of initial matrix is chosen,the bisymmetric solution with least norm can be obtained,and 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 双对称解 最佳逼近解 最小二乘解 

分 类 号：O151.21[理学—数学]