矩阵方程AX-BY=Z的最小二乘中心对称解及其最佳逼近  

Least-squares Solutions of Matrix Equation AX-BY=Z over Centrosymmetric Matrices and Its Optimal Approximation

作　　者：桂冰[1] 戴华[1] 

机构地区：[1]南京航空航天大学理学院

出　　处：《工程数学学报》2006年第5期849-855,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10271055)

摘　　要：本文研究矩阵方程AX-BY=Z的最小二乘中心对称解,给出了AX-BY=Z的最小二乘中心对称解的表达式,导出了AX-BY=Z有中心对称解的条件。讨论了在AX-BY=Z的最小二乘中心对称解集合中求与给定矩阵最佳逼近的解,并将所得结果应用于研究一类中心对称矩阵的广义特征值反问题。The least-squares solutions of the matrix equation AX - BY = Z with respect to centrosymmetric matrices A and B is considered. The general expression of the solution is given and some necessary and sufficient conditions are derived for the solvability of the matrix equation AX - BY = Z. The optimal approximation to given matrices from the least-squares solution set of AX - BY = Z is provided. These results are applied to solve an class of inverse generalized eigenvalue problem for centrosymmetric matrices.

关 键 词：矩阵方程 中心对称矩阵 最小二乘解 最佳逼近 反问题 

分 类 号：O241.6[理学—计算数学]