An alternative algorithm for the refinement of ULV decompositions

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dc.contributor.authorBarlow, Jesse L.
dc.contributor.authorErbay, Hasan
dc.contributor.authorSlapnicar, Ivan
dc.date.accessioned2020-06-25T17:40:55Z
dc.date.available2020-06-25T17:40:55Z
dc.date.issued2005
dc.departmentKırıkkale Üniversitesi
dc.descriptionSlapnicar, Ivan/0000-0002-8741-3988; Erbay, Hasan/0000-0002-7555-541X
dc.description.abstractThe ULV decomposition ( ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition ( SVD). It is useful in applications of the SVD such as principal components where we are interested in approximating a matrix by one of lower rank. It can be updated and downdated much more quickly than an SVD. In many instances, the ULVD must be refined to improve the approximation it gives for the important right singular subspaces or to improve the matrix approximation. Present algorithms to perform this refinement require O( mn) operations if the rank of the matrix is k, where k is very close to 0 or n, but these algorithms require O( mn(2)) operations otherwise. Presented here is an alternative refinement algorithm that requires O( mn) operations no matter what the rank is. Our tests show that this new refinement algorithm produces similar improvement in matrix approximation and in the subspaces. We also propose slight improvements on the error bounds on subspaces and singular values computed by the ULVD.en_US
dc.identifier.citationclosedAccessen_US
dc.identifier.doi10.1137/S0895479801372621
dc.identifier.endpage211en_US
dc.identifier.issn0895-4798
dc.identifier.issn1095-7162
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-33144456737
dc.identifier.scopusqualityQ2
dc.identifier.startpage198en_US
dc.identifier.urihttps://doi.org/10.1137/S0895479801372621
dc.identifier.urihttps://hdl.handle.net/20.500.12587/3584
dc.identifier.volume27en_US
dc.identifier.wosWOS:000232028400014
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSiam Publicationsen_US
dc.relation.ispartofSiam Journal On Matrix Analysis And Applications
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectsubspace approximationen_US
dc.subjectorthogonal decompositionsen_US
dc.subjectrefinementen_US
dc.titleAn alternative algorithm for the refinement of ULV decompositionsen_US
dc.typeArticle

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