Computing smallest singular triplets with implicitly restarted Lanczos bidiagonalization
type: Item
instance of: scholarly article
title: Computing smallest singular triplets with implicitly restarted Lanczos bidiagonalization
zbMATH Open document ID: 1049.65027
author: E. Kokiopoulou
author: C. Bekas
author: E. Gallopoulos
published in: Applied Numerical Mathematics
publication date: 2004-08-06T00:00:00Z
review text: This paper brings together Lanczos bidiagonalization, implicit restarts, deflation, and harmonic Ritz values for computing a few of the smallest singular values and vectors of a large sparse, possibly rectangular matrix. Although all these concepts are well known on their own, this approach is among the first to apply them together in the context of singular value problems. Several numerical experiments demonstrate that harmonic Ritz values and deflations are particularly important if the smallest singular values tend to be clustered. Moreover, it is shown that the proposed approach is, for all matrices under consideration, more efficient than some other methods. Meanwhile, however, the hunt on singular values has continued, and new, promising methods have been developed, for example by \textit{M. E. Hochstenbach} [Harmonic and refined extraction methods for the singular value problem, with applications in least squares problems, Preprint 1263, Dept. of Math., Utrecht University (2004)] as well as by \textit{J. Baglama} and \textit{L. Reichel} [Augmented implicitly restarted Lanczos bidiagonalization methods, Preprint (2004)].
reviewed by: Daniel Kressner
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 2081655
zbMATH Keywords: singular value decomposition
zbMATH Keywords: Lanczos method
zbMATH Keywords: implicit restarts
zbMATH Keywords: harmonic Ritz values
zbMATH Keywords: deflation
zbMATH Keywords: numerical experiments
describes a project that uses: ARPACK
describes a project that uses: IRAM
describes a project that uses: CRAIG
describes a project that uses: eigs
describes a project that uses: PROPACK
describes a project that uses: JDQR
describes a project that uses: Eigtool
describes a project that uses: testmatrix
describes a project that uses: LSQR
describes a project that uses: JDQZ
describes a project that uses: mctoolbox
MaRDI profile type: Publication
Wikidata QID: Q56659518
full work available at URL: j.apnum.2003.11.011
OpenAlex ID: W1975109850
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DOI: 10.1016/J.APNUM.2003.11.011
description: scientific article; zbMATH DE number 2081655