The inverse eigenvalue problem for Hermitian anti-reflexive matrices and its approximation

被引：17

作者：

Peng, ZY ^{[2
]}

机构：

[1] Cent S Univ, Dept Math, Changsha 410083, Peoples R China

[2] Hunan Univ Sci & Technol, Dept Math, Xiangtan 411201, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2005年 / 162卷 / 03期

关键词：

inverse eigenvalue problem; Hermitian anti-reflexive matrix; Matrix norm; best approximation;

D O I：

10.1016/j.amc.2004.03.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we first consider the inverse eigenvalue problem as follows: Find a matrix A with specified eigenpairs, where A is a Hermitian anti-reflexive matrix with respect to a given generalized reflection matrix J. The sufficient and necessary conditions are obtained, and it general representation of such a matrix is presented. We denote the set of Such matrices by S-A. Then the best approximation problem for the inverse eigenproblem is discussed. That is: given an arbitrary A*, find a matrix (A) over cap is an element of S-A which is nearest to A* in the Frobenius norm. We show that the best approximation is unique and provide an expression for this nearest matrix. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：1377 / 1389

页数：13

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