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General Solutions for a Class of Inverse Quadratic Eigenvalue Problems

Published online by Cambridge University Press:  28 May 2015

Xiaoqin Tan  and
Li Wang
Xiaoqin Tan*
Affiliation:
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
Li Wang*
Affiliation:
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
*
Corresponding author. Email: wlsha@163.com
Corresponding author. Email: wangli1@njnu.edu.cn
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Abstract

Based on various matrix decompositions, we compare different techniques for solving the inverse quadratic eigenvalue problem, where n × n real symmetric matrices M, C and K are constructed so that the quadratic pencil Q(λ) = λ2M + λC + K yields good approximations for the given k eigenpairs. We discuss the case where M is positive definite for 1 ≤ k ≤ n, and a general solution to this problem for n + 1 ≤ k ≤ 2n. The efficiency of our methods is illustrated by some numerical experiments.

Keywords

65F18Quadratic eigenvalue probleminverse quadratic eigenvalue problempartially prescribed spectral information
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 4 , Issue 1 , February 2014 , pp. 69 - 81
Copyright
Copyright © Global-Science Press 2014

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