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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

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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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