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

被引：0
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作者：
Zhen Yun Peng
Yuan Bei Deng
Jin Wang Liu
机构：
[1] Hunan University of Science and Technology,Department of Mathematics
[2] Central South University,Department of Mathematics
[3] Chinese Academy of Sciences,Institute of Computational Mathematics
[4] Hunan University of Science and Technology,Department of Mathematics
来源：
Acta Mathematica Sinica | 2006年 / 22卷
关键词：
Hermitian reflexive matrix; Hermitian anti–reflexive matrix; Matrix norm; Nearest matrix; 65F18; 65F30; 65F35;
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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 minA ‖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 SE. Then the matrix nearness problem for the matrix inverse problem is discussed. That is: Given an arbitrary A*, find a matrix  ∈ SE which 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：7
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