Spectral pollution and second‐order relative spectra for self‐adjoint operators

We consider the phenomenon of spectral pollution arising in calculation of spectra of self‐adjoint operators by projection methods. We suggest a strategy of dealing with spectral pollution by using the so‐called second‐order relative spectra. The effectiveness of the method is illustrated by a detai...

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Bibliographic Details
Published in:IMA journal of numerical analysis 2004-07, Vol.24 (3), p.393-416
Main Authors: Levitin, Michael, Shargorodsky, Eugene
Format: Article
Language:English
Subjects:
computation of eigenvalues
Exact sciences and technology
Mathematical analysis
Mathematics
Operator theory
projection methods
Sciences and techniques of general use
spectral pollution
spurious eigenvalues
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Summary:We consider the phenomenon of spectral pollution arising in calculation of spectra of self‐adjoint operators by projection methods. We suggest a strategy of dealing with spectral pollution by using the so‐called second‐order relative spectra. The effectiveness of the method is illustrated by a detailed analysis of two model examples.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/24.3.393