On the use of harmonic Ritz pairs in approximating internal eigenpairs

The goal of this paper is to increase our understanding of harmonic Rayleigh–Ritz for real symmetric matrices. We do this by discussing different, though related topics: a priori error analysis, a posteriori error analysis, a comparison with refined Rayleigh–Ritz and the selection of a suitable harm...

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Bibliographic Details
Published in:	Linear algebra and its applications Vol. 358; no. 1; pp. 115 - 137
Main Authors:	Sleijpen, Gerard L.G., Eshof, Jasper van den
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 2003
Subjects:	Harmonic Rayleigh–Ritz Interior eigenvalues Lehmann intervals Optimal eigenvalue bounds Rayleigh–Ritz Refined Ritz 65F50 Lehmann intervals 65F15 Rayleigh–Ritz Interior eigenvalues Refined Ritz Optimal eigenvalue bounds Harmonic Rayleigh–Ritz
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Summary:	The goal of this paper is to increase our understanding of harmonic Rayleigh–Ritz for real symmetric matrices. We do this by discussing different, though related topics: a priori error analysis, a posteriori error analysis, a comparison with refined Rayleigh–Ritz and the selection of a suitable harmonic Ritz vector.
ISSN:	0024-3795 1873-1856
DOI:	10.1016/S0024-3795(01)00480-3