反哈密顿矩阵的特征值反问题

广东工业大学学报 ›› 2011, Vol. 28 ›› Issue (1): 45-49.

反哈密顿矩阵的特征值反问题

广东工业大学应用数学学院,广东广州 510006

出版日期:2011-12-25 发布日期:2011-12-25
作者简介:莫荣华（1981-）,男，讲师，博士，主要研究方向为数值代数.
基金资助:
国家自然科学基金资助项目(10671077,10971075);广东省自然科学基金资助项目(06025061,9151063101000021)；广东工业大学校级博士启动基金资助项目

The Inverse Eigenvalue Problem of the Anti-Hamiltonian Matrices

Faculty of Applied Mathematics,Guangdong University of Technology,Guangzhou 510006,China

Online:2011-12-25 Published:2011-12-25

摘要/Abstract

摘要： 探讨了反哈密顿矩阵的特征值反问题,得到了该问题有解的充要条件、通解的表达式以及最小范数解.证明了其最佳逼近解的存在性和唯一性,建立了其最佳逼近解,并给出了求最佳逼近解的数值算法和算例.
特征值反问题;反哈密顿矩阵;奇异值分解;最佳逼近解

Abstract: It mainly discusses the inverse eigenvalue problem of the antiHamiltonian matrices.The necessary and sufficient solvability conditions for the problem are given.And the general form of solutions is presented.Furthermore,the optimal approximate solution to any given matrix is studied,such a solution is proved to be unique,and the formula to compute it is provided.Some numerical examples are given to demonstrate that the results are right and the algorithm is feasible.

Key words: Inverse eigenvalue problem; Anti-Hamiltonian matrix; Singular value decomposition(SVD); Optimal approximate solution

莫荣华, 黄志成. 反哈密顿矩阵的特征值反问题[J]. 广东工业大学学报, 2011, 28(1): 45-49.

MO Rong-Hua, HUANG Zhi-Cheng. The Inverse Eigenvalue Problem of the Anti-Hamiltonian Matrices[J]. Journal of Guangdong University of Technology, 2011, 28(1): 45-49.

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