谱约束下反自反矩阵的最佳逼近问题

数学物理学报 ›› 2009, Vol. 29 ›› Issue (2): 316-323.

谱约束下反自反矩阵的最佳逼近问题

关力, 张忠志, 谢冬秀

(东莞理工学院 |软件学院 |广东东莞 |523808)|(北京信息科技大学理学院 |北京 |100192)

收稿日期:2007-12-25 修回日期:2009-01-07 出版日期:2009-04-25 发布日期:2009-04-25
基金资助:
国家自然科学基金(10571012)和北京自然科学基金(1062005)资助

Optimal Approximation Problem of Antireflexive Matrices under the Spectral Restriction

GUAN Li, ZHANG Zhong-Zhi, XIE Dong-Xiu

(Department of Mathematics, Dongguan University of Technology, Guangdong Donguan 523808)|(School of Sciences, Beijing Information Science and Technology University, Beijing 100192)

Received:2007-12-25 Revised:2009-01-07 Online:2009-04-25 Published:2009-04-25
Supported by:
国家自然科学基金(10571012)和北京自然科学基金(1062005)资助

摘要/Abstract

摘要：

该文研究了反自反矩阵的逆特征值问题及其最佳逼近问题, 建立了反自反矩阵的逆特征值问题有解的充要条件, 得到了解的表达式.进一步, 对于任意给定的n阶复矩阵, 得到了相关最佳逼近问题解的表达式.

关键词: 反自反矩阵, 特征值反问题, 最佳逼近, 矩阵范数

Abstract:

In this paper, the inverse eigenvalue problem of antireflexive matrices and relevant optimal approximation
problem are considered. Some necessary and sufficient conditions of the solvability for the inverse eigenvalue problem are given. A general representation of the solution is presented for solvable case. Furthermore, for any given complex matrix of dimension n, an expression of solution for its optimal approximation is presented.

Key words: Antireflexive , matrix, Inverse eigenvalue problem, Optimal approximation, Matrix norm

中图分类号:

15A57

关力, 张忠志, 谢冬秀. 谱约束下反自反矩阵的最佳逼近问题[J]. 数学物理学报, 2009, 29(2): 316-323.

GUAN Li, ZHANG Zhong-Zhi, XIE Dong-Xiu. Optimal Approximation Problem of Antireflexive Matrices under the Spectral Restriction[J]. Acta mathematica scientia,Series A, 2009, 29(2): 316-323.

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