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

Tsung Ming Huang, Wen Wei Lin, Jiang Qian

Research output: Contribution to journalArticle

29 Citations (Scopus)

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
Publication statusPublished - 2008 Dec 1

Fingerprint

Quadratic Eigenvalue Problem
Vibration
Skew
Arnoldi
Invert
Finite Element Model
High Speed
Numerical Experiment

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

Structure-preserving algorithms for palindromic quadratic eigenvalue problems arising from vibration of fast trains. / Huang, Tsung Ming; Lin, Wen Wei; Qian, Jiang.

In: SIAM Journal on Matrix Analysis and Applications, Vol. 30, No. 4, 01.12.2008, p. 1566-1592.

Research output: Contribution to journalArticle

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