Palindromic eigenvalue problems: A brief survey

Eric King wah Chu, Tsung Ming Huang, Wen Wei Lin, Chin Tien Wu

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

The T-palindromic quadratic eigenvalue problem (λ2B + λC + A)x = 0, with A,B,C ε Cn×n, CT = C and BT = 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 Jun

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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