Spectral approximation for polynomial eigenvalue problems

Zhongjie Lu; Jacobus J.W. van der Vegt; Yan Xu

doi:10.1016/j.camwa.2018.06.007

Spectral approximation for polynomial eigenvalue problems

Zhongjie Lu (Corresponding Author), Jacobus J.W. van der Vegt, Yan Xu

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Abstract

In this paper, we extent the classical spectral approximation theory for compact and bounded operators to general linear operators, and then apply it to polynomial eigenvalue problems (PEP). We also study the essential spectrum in PEPs, and prove that this spectrum is stable under relatively compact perturbations. Based on this analysis, we give some suggestions to make algorithms for solving PEPs more efficient.

Original language	English
Pages (from-to)	1184 - 1197
Number of pages	14
Journal	Computers & mathematics with applications
Volume	76
Issue number	5
Early online date	20 Jun 2018
DOIs	https://doi.org/10.1016/j.camwa.2018.06.007
Publication status	Published - 1 Sept 2018

Keywords

22/4 OA procedure

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10.1016/j.camwa.2018.06.007

lu vegt xu 1-s2.0-S0898122118303316-mainFinal published version, 779 KBLicence: Taverne

Cite this

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AB - In this paper, we extent the classical spectral approximation theory for compact and bounded operators to general linear operators, and then apply it to polynomial eigenvalue problems (PEP). We also study the essential spectrum in PEPs, and prove that this spectrum is stable under relatively compact perturbations. Based on this analysis, we give some suggestions to make algorithms for solving PEPs more efficient.

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