Palindromic eigenvalue problems: A brief survey

Eric King wah Chu, Tsung-Min Hwang, Wen Wei Lin, Chin Tien Wu

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

The T-palindromic quadratic eigenvalue problem (λ 2 B + λC + A)x = 0, with A,B,C ε C n×n , C T = C and B T = A, governs the vibration behaviour of trains. Other palindromic eigenvalue problems, quadratic or higher order, arise from applications in surface acoustic wave filters, optimal control of discrete-time systems and crack modelling. Numerical solution of palindromic eigenvalue problems is challenging, with unacceptably low accuracy from the basic linearization approach. In this survey paper, we shall talk about the history of palindromic eigenvalue problems, in terms of their history, applications, numerical solution and generalization. We shall also speculate on some future directions of research.

Original languageEnglish
Pages (from-to)743-779
Number of pages37
JournalTaiwanese Journal of Mathematics
Volume14
Issue number3 A
DOIs
Publication statusPublished - 2010 Jan 1

Fingerprint

Quadratic Eigenvalue Problem
Eigenvalue Problem
Numerical Solution
Surface Acoustic Wave
Discrete-time Systems
Linearization
Crack
Optimal Control
Vibration
Higher Order
Filter
Modeling
History
Generalization

Keywords

  • Crack
  • Crawford number
  • Eigenvalue
  • Eigenvector
  • Matrix polynomial
  • Palindromic eigenvalue problem
  • SAW filter
  • Train vibration

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Palindromic eigenvalue problems : A brief survey. / Chu, Eric King wah; Hwang, Tsung-Min; Lin, Wen Wei; Wu, Chin Tien.

In: Taiwanese Journal of Mathematics, Vol. 14, No. 3 A, 01.01.2010, p. 743-779.

Research output: Contribution to journalArticle

Chu, Eric King wah ; Hwang, Tsung-Min ; Lin, Wen Wei ; Wu, Chin Tien. / Palindromic eigenvalue problems : A brief survey. In: Taiwanese Journal of Mathematics. 2010 ; Vol. 14, No. 3 A. pp. 743-779.
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