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

• 数学 统计学 • 上一篇    下一篇

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. 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-hui1,2, WEI Mu-sheng1   

  1. 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: 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.

关键词: 标准相关分解, 加权最小二乘解, 最佳逼近解, 标准相关分解, 加权最小二乘解, 最佳逼近解

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

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