Structured backward error for palindromic polynomial eigenvalue problems

Ren Cang Li; Wen Wei Lin; Chern Shuh Wang

doi:10.1007/s00211-010-0297-4

Structured backward error for palindromic polynomial eigenvalue problems

Ren Cang Li, Wen Wei Lin, Chern Shuh Wang

Department of Mathematics

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

14 Citations (Scopus)

Abstract

A detailed structured backward error analysis for four kinds of palindromic polynomial eigenvalue problems (PPEP). where * is one of the two actions: transpose and conjugate transpose, and ε ∈ {±1}.Each of them has its application background with the case * taking transpose and ε = 1 attracting a great deal of attention lately because of its application in the fast train modeling. Computable formulas and bounds for the structured backward errors are obtained. The analysis reveals distinctive features of PPEP from general polynomial eigenvalue problems (PEP) investigated by Tisseur (Linear Algebra Appl 309:339-361, 2000) and by Liu and Wang (Appl Math Comput 165:405-417, 2005).

Original language	English
Pages (from-to)	95-122
Number of pages	28
Journal	Numerische Mathematik
Volume	116
Issue number	1
DOIs	https://doi.org/10.1007/s00211-010-0297-4
Publication status	Published - 2010

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1007/s00211-010-0297-4

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AU - Lin, Wen Wei

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AB - A detailed structured backward error analysis for four kinds of palindromic polynomial eigenvalue problems (PPEP). where * is one of the two actions: transpose and conjugate transpose, and ε ∈ {±1}.Each of them has its application background with the case * taking transpose and ε = 1 attracting a great deal of attention lately because of its application in the fast train modeling. Computable formulas and bounds for the structured backward errors are obtained. The analysis reveals distinctive features of PPEP from general polynomial eigenvalue problems (PEP) investigated by Tisseur (Linear Algebra Appl 309:339-361, 2000) and by Liu and Wang (Appl Math Comput 165:405-417, 2005).

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Structured backward error for palindromic polynomial eigenvalue problems

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