Least-Squares Solution of Inverse Problem for Hermitian Anti-reflexive Matrices and Its Appoximation

被引：2
|
作者：
Zhen Yun PENG [1 ,2 ]
Yuan Bei DENG [3 ]
Jin Wang LIU [1 ]
机构：
[1] Department of Mathematics, Hunan University of Science and Technology
[2] Department of Mathematics, Central South University
[3] Institute of Computational Mathematics, Chinese Academy of Sciences
来源：
ActaMathematicaSinica(EnglishSeries) | 2006年 / 22卷 / 02期
基金：
中国博士后科学基金;
关键词：
hermitian reflexive matrix; hermitian anti-reflexive matrix; matrix norm; nearest matrix;
D O I：
暂无
中图分类号：
O151.21 [矩阵论];
学科分类号：
摘要：
In this paper, we first consider the least-squares solution of the matrix inverse problem as follows: Find a hermitian anti-reflexive matrix corresponding to a given generalized reflection matrix J such that for given matrices X, B we have min‖AX-B‖. The existence theorems are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by S. Then the matrix nearness problem for the matrix inverse problem is discussed. That is: Given an arbitrary A~*, find a matrix A ∈Swhich is nearest to A~* in Frobenius norm. We show that the nearest matrix is unique and provide an expression for this nearest matrix.
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页码：477 / 484
页数：8
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