Accuracy of singular vectors obtained by projection-based SVD methods
type: Item
instance of: scholarly article
title: Accuracy of singular vectors obtained by projection-based SVD methods
zbMATH Open document ID: 1386.65116
author: Yuji Nakatsukasa
published in: BIT
publication date: 2018-01-12T00:00:00Z
review text: An alternative approach for the computation of an approximate SVD of a large-scale matrix is proposed in this paper. The numerical approach of an SVD of a large-scale matrix is based on its projection onto lower-dimensional trial subspaces from both sides and the computation of the SVD of the small projected matrix that is again projected back to the original space. Following this basic approach, a low-rank approximate SVD to the original matrix is obtained and by extracting subsets from the approximate SVD, the approximate left and right singular subspaces are determined. The authors propose the estimation of the quality of the extraction process of the subsets from the approximate SVD in terms of the accuracy of the approximate singular subspaces, measured by the angle between the exact and extracted subspaces in relation to the angle between the exact and trial subspaces. This estimation leads to the conclusion that the extracted approximate subspaces are optimal usually to within a modest constant.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 6825307
zbMATH Keywords: SVD
zbMATH Keywords: subspace angle
zbMATH Keywords: singular vectors
Wikidata QID: Q59614884
describes a project that uses: JDQR
describes a project that uses: JDQZ
describes a project that uses: mftoolbox
MaRDI profile type: Publication
full work available at URL: s10543-017-0665-x
OpenAlex ID: W2654090051
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DOI: 10.1007/S10543-017-0665-X
description: scientific article; zbMATH DE number 6825307