A note on unimodular eigenvalues for palindromic eigenvalue problems

We consider the occurrence of unimodular eigenvalues for palindromic eigenvalue problems associated with the matrix polynomial where A i *=A n−i with M* ≡ M T , M H or . From the properties of palindromic eigenvalues and their characteristic polynomials, we show that eigenvalues are not generically...

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Bibliographic Details
Published inInternational journal of computer mathematics Vol. 89; no. 17; pp. 2385 - 2391
Main Authors Chiang, Chun-Yueh, King-wah Chu, Eric, Weng, Chang-Yi
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.11.2012
Taylor & Francis Ltd
Subjects
Computer simulation
Cracks
Eigenvalues
Mathematical models
Mathematical problems
Matrix
Numerical analysis
palindromic eigenvalue problem
Polynomials
Simulation
structure-preserving doubling algorithm
Trains
unimodular eigenvalue
Vibration
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Summary:We consider the occurrence of unimodular eigenvalues for palindromic eigenvalue problems associated with the matrix polynomial where A i *=A n−i with M* ≡ M T , M H or . From the properties of palindromic eigenvalues and their characteristic polynomials, we show that eigenvalues are not generically excluded from the unit circle, thus occurring quite often, except for the complex transpose case when P n is complex and M* ≡ M T . This behaviour is observed in numerical simulations and has important implications on several applications such as the vibration of fast trains, surface acoustic wave filters, stability of time-delay systems and crack modelling.
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ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2012.709626