| 矩阵方程AX＋XB=C的双对称解及其最佳逼近 |
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| 引用本文： | 刘畔畔,李庆春.矩阵方程AX＋XB=C的双对称解及其最佳逼近[J].大学数学,2011,27(4):93-98. |
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| 作者姓名： | 刘畔畔 李庆春 |
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| 作者单位： | 北华大学数学学院,吉林吉林,132013 |
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| 基金项目： | 国家“973”项目基金 |
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| 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...
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| 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 |
The Bisymmetric Solution of Matrix Equation AX＋XB=C and Its Optimal Approximation |
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| LIU Pan-pan,LI Qing-chun.The Bisymmetric Solution of Matrix Equation AX＋XB=C and Its Optimal Approximation[J].College Mathematics,2011,27(4):93-98. |
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| Authors: | LIU Pan-pan LI Qing-chun |
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| Institution: | LIU Pan-pan,LI Qing-chun(Mathematical College,Beihua University,Jilin Jilin 132013,China) |
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| Abstract: | 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. |
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| Keywords: | linear matrix equation iterative method bisymmetric solution optimal approximation solution least-squares solution |
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