A dual optimization approach to inverse quadratic eigenvalue problems with partial eigenstructure

Z.-J. Bai, D. Chu, Defeng Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

26 Citations (Scopus)

Abstract

The inverse quadratic eigenvalue problem (IQEP) arises in the field of structural dynamics. It aims to find three symmetric matrices, known as the mass, the damping, and the stiffness matrices, such that they are closest to the given analytical matrices and satisfy the measured data. The difficulty of this problem lies in the fact that in applications the mass matrix should be positive definite and the stiffness matrix positive semidefinite. Based on an equivalent dual optimization version of the IQEP, we present a quadratically convergent Newton-type method. Our numerical experiments confirm the high efficiency of the proposed method. © 2007 Society for Industrial and Applied Mathematics.
Original languageEnglish
Pages (from-to)2531-2561
Number of pages31
JournalSIAM Journal on Scientific Computing
Volume29
Issue number6
DOIs
Publication statusPublished - 1 Dec 2007
Externally publishedYes

Keywords

  • Inverse eigenvalue problem
  • Nonlinear optimization
  • Partial eigenstructure
  • Quadratic eigenvalue problem

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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