Structure-preserving algorithms for palindromic quadratic eigenvalue problems arising from vibration of fast trains

Tsung Ming Huang*, Wen-Wei Lin, Jiang Qian

*Corresponding author for this work

Research output: Contribution to journalArticle

30 Scopus citations

Abstract

In this paper, based on Patel's algorithm (1993), we propose a structure-preserving algorithm or solving palindromic quadratic eigenvalue problems (QEPs). We also show the relationship between the structure-preserving algorithm and the URV-based structure-preserving algorithm by Schröder (2007). For large sparse palindromic QEPs, we develop a generalized Τ-skew-Hamiltonian implicitly restarted shift-and-invert Arnoldi algorithm for solving the resulting Τ-skew-Hamiltonian pencils. Numerical experiments show that our proposed structure-preserving algorithms perform well on the palindromic QEP arising from a finite element model of high-speed trains and rails.

Original languageEnglish
Pages (from-to)1566-1592
Number of pages27
JournalSIAM Journal on Matrix Analysis and Applications
Volume30
Issue number4
DOIs
StatePublished - 1 Dec 2008

Keywords

  • Τ-skew-Hamiltonian Pencil
  • Τ-symplectic pencil
  • Palindromic quadratic eigenvalue problem

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