子矩阵约束下的埃尔米特广义反汉密尔顿矩阵特征值反问题及其最佳逼近

数学物理学报 ›› 2011, Vol. 31 ›› Issue (3): 691-701.

子矩阵约束下的埃尔米特广义反汉密尔顿矩阵特征值反问题及其最佳逼近

莫荣华¹, 黎稳²

1.广东工业大学应用数学学院广州 510006|2.华南师范大学数学科学学院广州 510631

收稿日期:2009-04-22 修回日期:2010-08-27 出版日期:2011-06-25 发布日期:2011-06-25
基金资助:
国家自然科学基金(10671077, 10971075)、广东省自然科学基金(06025061, 9151063101000021)和广东工业大学校级博士启动基金(103005)资助

The Inverse Eigenvalue Problem of Hermitian and Generalized Skew-Hamiltonian |Matrices with a Submatrix Constraint and Its Approximation

MO Rong-Hua¹, LI Wen²

1.Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006|2.School of Mathematical Sciences, South China Normal University, Guangzhou 510631

Received:2009-04-22 Revised:2010-08-27 Online:2011-06-25 Published:2011-06-25
Supported by:
国家自然科学基金(10671077, 10971075)、广东省自然科学基金(06025061, 9151063101000021)和广东工业大学校级博士启动基金(103005)资助

摘要/Abstract

摘要：

该文研究了子矩阵约束下埃尔米特广义反汉密尔顿矩阵特征值反问题, 得到了该问题解的表达式. 证明了该约束下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.

关键词: 反问题, 埃尔米特矩阵, 广义反汉密尔顿矩阵, 子矩阵约束, 最佳逼近

Abstract:

In this paper, the authors consider the inverse eigenvalue problem of Hermitian and generalized skew-Hamiltonian matrices with a submatrix constraint, provide an expression of the solution. The authors also show that the best approximation is existed and unique and provide an expression of the solution. A numerical algorithm is given, and a numerical example is provided to illustrate the results.

Key words: Inverse problem, Hermitian matrix, Generalized skew-Hamiltonian matrix, Submatrix constraint, Best approximation

中图分类号:

65F10

莫荣华, 黎稳. 子矩阵约束下的埃尔米特广义反汉密尔顿矩阵特征值反问题及其最佳逼近[J]. 数学物理学报, 2011, 31(3): 691-701.

MO Rong-Hua, LI Wen. The Inverse Eigenvalue Problem of Hermitian and Generalized Skew-Hamiltonian |Matrices with a Submatrix Constraint and Its Approximation[J]. Acta mathematica scientia,Series A, 2011, 31(3): 691-701.

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