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| 子矩阵约束下矩阵方程AXB=E的极小范数最小二乘对称解 | |
| 引用本文： | 王明辉,魏木生,姜同松.子矩阵约束下矩阵方程AXB=E的极小范数最小二乘对称解[J].计算数学,2007,29(2):147-154. |
| 作者姓名： | 王明辉 魏木生 姜同松 |
| 作者单位： | 1. 曲阜师范大学数学系,山东曲阜,273165;华东师范大学数学系,上海,200062 2. 华东师范大学数学系,上海,200062 3. 临沂师范学院数学系,山东,临沂,276005 |
| 摘 要： | 本文主要研究了任意子矩阵约束下矩阵方程AXB=E的极小范数最小二乘对称解问题,方法是借助于子空间的基将约束问题转化为非约束问题,可以应用到线性矩阵方程的所有子空间约束解问题． |
| 关 键 词： | 矩阵方程 Frobenius范数 极小范数解 正交基 |
| 修稿时间： | 2005-11-20 |
THE MINIMUM-NORM LEAST-SQUARES SYMMETRIC SOLUTIONS OF MATRIX EQUATION AXB=E WITH A SUBMATRIX CONSTRAINT |
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| Wang Minghui,Wei Musheng,Jiang Tongsong.THE MINIMUM-NORM LEAST-SQUARES SYMMETRIC SOLUTIONS OF MATRIX EQUATION AXB=E WITH A SUBMATRIX CONSTRAINT[J].Mathematica Numerica Sinica,2007,29(2):147-154. | |
| Authors: | Wang Minghui Wei Musheng Jiang Tongsong |
| Institution: | 1.Department of Mathematics, Qufu Normal University, Qufu 273165, Shandong, China;2. Department of Mathematics, East China Normal University, Shanghai 200062, China;3.Department of Mathematics, Linyi Normal University, Linyi 276005, Shandong, China |
| Abstract: | This paper studys the minimum-norm least-squares symmetric solutions of matrix equation AXB = E with a arbitrary submatrix constraint. By the basis vectors of subspace, the constraint problem is transformed into a unconstraint problem. This method can be applied to many similar problems. |
| Keywords: | matrix equation Frobeinus norm minimum-norm solution orthogonal basis |
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