Numerical solution of quadratic eigenvalue problems with structure-preserving methods

Tsung Min Hwang, Wen Wei Lin, Volker Mehrmann

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

Numerical methods for the solution of large scale structured quadratic elgenvalue problems are discussed. We describe a new extraction procedure for the computation of eigenvectors and invariant subspaces of skew-Hamiltonian/Hamiltonian pencils using the recently proposed skew-Hamiltonian isotropic implicitly restarted Arnoldi method (SHIRA). As an application we discuss damped gyroscopic systems. For this problem we first solve the eigenvalue problem for the undamped system using the structure-preserving method and then use the quadratic Jacobi-Davidson method as correction procedure. We also illustrate the properties of the new approach for several other application problems.

Original languageEnglish
Pages (from-to)1283-1302
Number of pages20
JournalSIAM Journal on Scientific Computing
Volume24
Issue number4
DOIs
Publication statusPublished - 2003 Jan 1

Fingerprint

Quadratic Eigenvalue Problem
Hamiltonians
Numerical Solution
Skew
Jacobi-Davidson Method
Arnoldi Method
Invariant Subspace
Eigenvalues and eigenfunctions
Damped
Eigenvector
Eigenvalue Problem
Numerical methods
Numerical Methods

Keywords

  • Gyroscopic system
  • Invariant subspace
  • Nonequivalence deflation technique
  • Quadratic Jacobi-Davidson method
  • Quadratic eigenvalue problems
  • Skew-Hamiltonian/Hamiltonian pencils

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Numerical solution of quadratic eigenvalue problems with structure-preserving methods. / Hwang, Tsung Min; Lin, Wen Wei; Mehrmann, Volker.

In: SIAM Journal on Scientific Computing, Vol. 24, No. 4, 01.01.2003, p. 1283-1302.

Research output: Contribution to journalArticle

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