关于矩阵方程AXB=E的加权最小二乘Hermite解  

ON WEIGHTED LEAST-SQUARES HERMITE SOLUTION OF MATRIX EQUATION AXB = E

作　　者：王明辉[1,2] 魏木生[1] 

机构地区：[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

出　　处：《计算数学》2004年第2期129-136,共8页Mathematica Numerica Sinica

基　　金：国家自然科学基金(编号: 10371044);上海重点学科科研基金资助项目.

摘　　要：In this paper, we discuss the matrix equation AXB = C. We obtain a terse expression of weighted least-squares solution by applying the canonical correlation decomposition(CCD), we discuss the sufficient and necessary conditions for existence of Hermitian solutions, and derive a general form of the Hermite solutions.We also derive the expression of the optimal approximation solution in the set of Hermite soluti6ns to given matrix.In this paper, we discuss the matrix equation AXB = C. We obtain a terse expression of weighted least-squares solution by applying the canonical correlation decomposition(CCD). we discuss the sufficient and necessary conditions for existence of Hermitian solutions, and derive a general form of the Hermite solutions. We also derive the expression of the optimal approximation solution in the set of Hermite solutions to given matrix.

关 键 词：标准相关分解 加权最小二乘解 最佳逼近解 矩阵方程 

分 类 号：O241[理学—计算数学]