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PERTURBATION RESULTS RELATED TO PALINDROMIC EIGENVALUE PROBLEMS

Part of: Numerical linear algebra Basic linear algebra

Published online by Cambridge University Press:  01 July 2008

E. K.-W. CHU ,
W.-W. Lin  and
C.-S. Wang
E. K.-W. CHU*
Affiliation:
School of Mathematical Sciences, Building 28, Monash University, VIC 3800, Australia (email: eric.chu@sci.monash.edu.au)
W.-W. Lin
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan (email: wwlin@am.cthu.edu.tw)
C.-S. Wang
Affiliation:
Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan (email: cswang@math.ncku.edu.tw)
*
✉For correspondence; e-mail: eric.chu@sci.monash.edu.au
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Abstract

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We investigate the perturbation of the palindromic eigenvalue problem for the matrix quadratic $P(\lambda ) = \lambda ^2 A_1^\star + \lambda A_0 + A_1$ with A0,A1∈𝒞n×n and $A_0^\star = A_0$ (where $\star = T$ or H). The perturbation of eigenvalues in the context of general matrix polynomials, palindromic pencils, (semi-Schur) anti-triangular canonical forms and differentiation is discussed.

Keywords

anti-triangular formeigenvalueeigenvectormatrix polynomialpalindromic eigenvalue problempalindromic linearizationpalindromic pencilperturbation

MSC classification

Secondary: 15A18: Eigenvalues, singular values, and eigenvectors 15A22: Matrix pencils 65F15: Eigenvalues, eigenvectors

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 1 , July 2008 , pp. 87 - 100
Copyright
Copyright © Australian Mathematical Society 2009

References

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