The palindromic generalized eigenvalue problem Az.ast;x= λAx: Numerical solution and applications

Tiexiang Li, Chun Yueh Chiang, Eric King Wah Chu, Wen-Wei Lin

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8 Scopus citations


In this paper, we propose the palindromic doubling algorithm (PDA) for the palindromic generalized eigenvalue problem (PGEP) Az.astx=λAx. We establish a complete convergence theory of the PDA for PGEPs without unimodular eigenvalues, or with unimodular eigenvalues of partial multiplicities two (one or two for eigenvalue 1). Some important applications from the vibration analysis and the optimal control for singular descriptor linear systems will be presented to illustrate the feasibility and efficiency of the PDA.

Original languageEnglish
Pages (from-to)2269-2284
Number of pages16
JournalLinear Algebra and Its Applications
Issue number11
StatePublished - 1 Jun 2011


  • Doubling algorithm
  • Palindromic generalized eigenvalue problem
  • Singular descriptor system

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