Perturbation results related to palindromic eigenvalue problems

E. K.W. Chu; Wen-Wei Lin; C. S. Wang

doi:10.1017/S144618110800031X

Perturbation results related to palindromic eigenvalue problems

E. K.W. Chu, Wen-Wei Lin, C. S. Wang

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We investigate the perturbation of the palindromic eigenvalue problem for the matrix quadratic P(λ) = λ² A₁* + λ A₀ + A₁ with A₀,A₁ C ^n×n and AM₀* = A₀ (where * = 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.

Original language	English
Pages (from-to)	87-100
Number of pages	14
Journal	ANZIAM Journal
Volume	50
Issue number	1
DOIs	https://doi.org/10.1017/S144618110800031X
State	Published - 1 Dec 2009

Keywords

anti-triangular form
eigenvalue
eigenvector
matrix polynomial
palindromic eigenvalue problem
palindromic linearization
palindromic pencil
perturbation

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10.1017/S144618110800031X

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title = "Perturbation results related to palindromic eigenvalue problems",

abstract = "We investigate the perturbation of the palindromic eigenvalue problem for the matrix quadratic P(λ) = λ2 A1* + λ A0 + A1 with A0,A1 C n×n and AM0* = A0 (where * = 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 form, eigenvalue, eigenvector, matrix polynomial, palindromic eigenvalue problem, palindromic linearization, palindromic pencil, perturbation",

author = "Chu, {E. K.W.} and Wen-Wei Lin and Wang, {C. S.}",

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AU - Chu, E. K.W.

AU - Lin, Wen-Wei

AU - Wang, C. S.

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Y1 - 2009/12/1

N2 - We investigate the perturbation of the palindromic eigenvalue problem for the matrix quadratic P(λ) = λ2 A1* + λ A0 + A1 with A0,A1 C n×n and AM0* = A0 (where * = 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.

AB - We investigate the perturbation of the palindromic eigenvalue problem for the matrix quadratic P(λ) = λ2 A1* + λ A0 + A1 with A0,A1 C n×n and AM0* = A0 (where * = 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.

KW - anti-triangular form

KW - eigenvalue

KW - eigenvector

KW - matrix polynomial

KW - palindromic eigenvalue problem

KW - palindromic linearization

KW - palindromic pencil

KW - perturbation

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DO - 10.1017/S144618110800031X

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SP - 87

EP - 100

JO - ANZIAM Journal

JF - ANZIAM Journal

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