矩阵方程AXB=E的加权最小二乘Skew-Hermite解

华东师范大学学报(自然科学版) ›› 2004, Vol. 2004 ›› Issue (1): 22-28.

矩阵方程AXB=E的加权最小二乘Skew-Hermite解

王明辉^1,2, 魏木生¹

1.华东师范大学数学系，上海 200062; 2.曲阜师范大学数学系，山东 273165

收稿日期:2002-05-10 修回日期:2002-11-28 出版日期:2004-03-25 发布日期:2004-03-25
通讯作者: 王明辉

On Weighted Least-squares Skew-Hermite Solution of Matrix Equation AXB=E

WANG Ming-hui^1,2, WEI Mu-sheng¹

1. Department of Mathematics，East China Normal University，Shanghai 200062, China2. Department of Mathematic，QuFu Normal University，Shandong 273165, China

Received:2002-05-10 Revised:2002-11-28 Online:2004-03-25 Published:2004-03-25
Contact: WANG Ming-hui

摘要/Abstract

摘要： 作者运用CCD的手段，得到了矩阵方程AXB=E的极小范数加以最小二乘Skew-Hermite解的表达式和方程有Skew-Hermite解的充要条件，而且也引伸出给定矩阵在Skew-Hermite解集中的最佳逼近解的表达式.

Abstract: Using CCD of a matrix pair, this paper obtains the expression of the weighted least-squares Skew-Hermite solution with minimum norm of matrix equation AXB二E and the necessary and sufficient conditions for the existence of its Skew-Hermite solution. Also, in the solution set of matrix equation, the
expression of the optimal approximation solution to given matriix is derived.

Key words: weighted least-squares solution, optimal approximation, CCD, weighted least-squares solution, optimal approximation

中图分类号:

0151. 21

王明辉;魏木生. 矩阵方程AXB=E的加权最小二乘Skew-Hermite解[J]. 华东师范大学学报(自然科学版), 2004, 2004(1): 22-28.

WANG Ming-hui;WEI Mu-sheng. On Weighted Least-squares Skew-Hermite Solution of Matrix Equation AXB=E[J]. Journal of East China Normal University(Natural Sc, 2004, 2004(1): 22-28.