PALINDROMIC EIGENVALUE PROBLEMS: A BRIEF SURVEY

The T-palindromic quadratic eigenvalue problem (λ²B + λC + A)x = 0, with A, B, C ∊, 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 discr...

Full description

Saved in:
Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 14; no. 3A; pp. 743 - 779
Main Authors Chu, Eric King-wah, 朱景華, Huang, Tsung-Ming, 黃聰明, Lin, Wen-Wei, 林文偉, Wu, Chin-Tien, 吳金典
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China (Taiwan) 01.06.2010
Subjects
Eigenvalues
Linearization
Mathematics
Matrices
Pencils
Polynomials
Preprints
Spectral theory
Vibration
Online AccessGet full text

Cover

More Information
Summary:The T-palindromic quadratic eigenvalue problem (λ²B + λC + A)x = 0, with A, B, C ∊, 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.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500405865