一类对称正交反对称矩阵反问题的最佳逼近  

The Optimal Approximation to the Inverse Problems for Symmetric Ortho-Anti-Symmetric Matrices

作　　者：于蕾[1] 张凯院[2] 周丙常[2] 

机构地区：[1]西北工业大学自动化学院,西安710072 [2]西北工业大学理学院,西安710072

出　　处：《数学的实践与认识》2008年第8期158-163,共6页Mathematics in Practice and Theory

基　　金：陕西省自然科学基金(2004CS110002)

摘　　要：讨论了一类对称正交反对称反问题的最佳逼近.利用对称正交反对称矩阵的特殊性质,给出了矩阵方程AX=B有对称正交反对称解的充要条件以及解的一般表达式;证明最佳逼近解的存在惟一性并给出其表达式;最后给出计算任意矩阵的最佳逼近解的数值方法及算例.This paper discusses the inverse problem and the optimal approximation to the symmetric ortho-anti-symmetric matrices. By the properties of this kind of matrix, the necessary and sufficient conditions for the solvability of matrix equation AX=B and the general form of the symmetric ortho-anti-symmetric solutions are given. In addition, the existence and uniqueness of the optimal approximation is proved. The expression of the optimal approximation solution to the given matrix is presented. Numerical methods of the optimal approximation to a given matrix and numerical experiments are described.

关 键 词：矩阵方程 对称正交反对称矩阵 最佳逼近 

分 类 号：O241.6[理学—计算数学] O151.21[理学—数学]