二次特征值反问题的对称次反对称解及其最佳逼近

J4 ›› 2009, Vol. 47 ›› Issue (6): 1185-1190.

二次特征值反问题的对称次反对称解及其最佳逼近

郭丽杰, 周硕

东北电力大学理学院, 吉林吉林 132012

收稿日期:2009-02-19 出版日期:2009-11-26 发布日期:2010-01-07
通讯作者: 周硕 E-mail:zhoushuo@163.com.

Symmetric and Skew Antisymmetric Solution of |InverseQuadratic Eigenvalue Problem and Its Optimal Approximation

GUO Lijie, ZHOU Shuo

College of Science, Northeast Dianli University, Jilin 132012, Jilin Province, China

Received:2009-02-19 Online:2009-11-26 Published:2010-01-07
Contact: ZHOU Shuo E-mail:zhoushuo@163.com.

摘要/Abstract

摘要：

利用矩阵的奇异值分解和矩阵的Kronecker乘积, 讨论构造对称次反对称矩阵M,C和K, 使得二次约束Q(λ)=λ²M+λC+K具有给定特征值和特征向量的特征值反问题. 首先证明反问题是可解的, 并给出了解集S_MCK的通式. 进而考虑了解集S_MCK中对给定矩阵的最佳逼近问题, 得到了最佳逼近解.

关键词: 二次特征值；对称次反对称矩阵；反问题；最佳逼近；奇异值分解

Abstract:

The inverse eigenvalue problem of constructing symmetric and skew antisymmetric matrices M,C and K of size n for the quadratic pencil Q(λ)=λ²M+λC+K so that Q(λ) has a prescribed subset of eigenvalues and eigenvectors was considered by means of singular value decomposition of matrix and Kronecker product of matrices. The problem was firstly improved to be solvable and the general expression of the solution to the problem was provided. The optimal approximation problem a
ssociated with S_MCK was posed, that is, to find the nearest triple matrix from S_MCK. The existence and uniqueness of the optimal approximation problem was discussed and the exoression was provided for the optimal approximation problem.

Key words: quadratic eigenvalue problem, symmetric and skew antisymmetric matrix; , inverse problem, optimal approximation, singular value decomposition

中图分类号:

O242.25

郭丽杰, 周硕. 二次特征值反问题的对称次反对称解及其最佳逼近[J]. J4, 2009, 47(6): 1185-1190.

GUO Lijie, ZHOU Shuo. Symmetric and Skew Antisymmetric Solution of |InverseQuadratic Eigenvalue Problem and Its Optimal Approximation[J]. J4, 2009, 47(6): 1185-1190.