矩阵方程AX+BY+CZ=F广义中心对称最小二乘解  

The Generalized Centro-symmetric Solution of a Matrix Equation And Its Optimal Approximation

作　　者：张远福[1] 周金贵[1] 叶正道[1] 

机构地区：[1]九江学院理学院

出　　处：《科技通报》2012年第11期4-7,共4页Bulletin of Science and Technology

摘　　要：研究矩阵方程AX+BY+CZ=F广义中心对称解,给出了AX+BY+CZ=F的最小二乘广义中心对称解的表达式,导出了AX+BY+CZ=F有广义中心对称解的条件。讨论了在AX+BY+CZ=F最小二乘广义中心对称解集合中求与给定矩阵最佳逼近解。In this paper,the least-squares solution of the matrix equation AX＋BY＋CZ=F with respect to Generalized Centrosymmetric Matrices A 、B and C are considered.The general expression of the solution is given and some conditions are derived for the solvability of the matrix equation AX＋BY＋CZ=F over Generalized Centro-symmetric Matrices.The optimal approximation of the least-squares solution set of AX＋BY＋CZ=F is provided.

关 键 词：矩阵方程 广义中心对称矩阵 最小二乘 最佳逼近 

分 类 号：O241.6[理学—计算数学]