矩阵方程AXA^T+BYB^T=C的双对称最小二乘解及其最佳逼近  

An Iterative Method for the Least Squares Bisymmetric Solutions of the Linear Matrix Equation AXA^T+BYB^T=C

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：《大学数学》2012年第6期67-73,共7页College Mathematics

基　　金：宁夏大学科学研究基金(NDZR10-75;ZR1102);宁夏自然科学基金(NZ12106)

摘　　要：基于共轭梯度法的思想,通过特殊的变形,建立了一类求矩阵方程AXAT+BYBT=C的双对称最小二乘解的迭代算法.对任意的初始双对称矩阵.在没有舍入误差的情况下,经过有限步迭代得到它的双对称最小二乘解;在选取特殊的初始双对称矩阵时,能得到它的的极小范数双对称最小二乘解.另外,给定任意矩阵,利用此方法可得到它的最佳逼近双对称解,数值例子表明,这种方法是有效的.On the base of conjugate gradient method, using special transformation, an iterative method is presented to solve the least squares bisymmetric solution pair of the linear matrix equation AXA^T＋BYB^T=C.By this iterative method, the least squares bisymmetric solution pair can be obtained within finite iterative steps in the absence of roundoff errors, and minimum norm of the least squares solution pair can be obtained by choosing a special kind of initial matrix pair, In addition, the unique optimal approximation solution pair 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 双对称最小二乘解 极小范数解 最佳逼近解 

分 类 号：O175.13[理学—数学]