Show simple item record

dc.contributor.authorMartinsson, Gunnar
dc.contributor.authorQuintana Ortí, Gregorio
dc.contributor.authorHeavner, Nathan
dc.contributor.authorVan de Geijn, Robert A.
dc.date.accessioned2018-01-18T19:49:06Z
dc.date.available2018-01-18T19:49:06Z
dc.date.issued2017
dc.identifier.citationMartinsson, P. G., Quintana OrtÍ, G., Heavner, N., & van de Geijn, R. (2017). Householder QR Factorization With Randomization for Column Pivoting (HQRRP). SIAM Journal on Scientific Computing, 39(2), C96-C115.ca_CA
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.urihttp://hdl.handle.net/10234/171920
dc.description.abstractA fundamental problem when adding column pivoting to the Householder QR fac- torization is that only about half of the computation can be cast in terms of high performing matrix- matrix multiplications, which greatly limits the bene ts that can be derived from so-called blocking of algorithms. This paper describes a technique for selecting groups of pivot vectors by means of randomized projections. It is demonstrated that the asymptotic op count for the proposed method is 2mn2 �����(2=3)n3 for an m n matrix, identical to that of the best classical unblocked Householder QR factorization algorithm (with or without pivoting). Experiments demonstrate acceleration in speed of close to an order of magnitude relative to the geqp3 function in LAPACK, when executed on a modern CPU with multiple cores. Further, experiments demonstrate that the quality of the randomized pivot selection strategy is roughly the same as that of classical column pivoting. The described algorithm is made available under Open Source license and can be used with LAPACK or libflame.ca_CA
dc.format.extent20 p.ca_CA
dc.format.mimetypeapplication/pdfca_CA
dc.language.isoengca_CA
dc.publisherSociety for Industrial and Applied Mathematicsca_CA
dc.relation.isPartOfSIAM Journal on Scientific Computing, 2017, vol. 39, no 2, p. C96-C115.ca_CA
dc.titleHouseholder QR Factorization With Randomization for Column Pivoting (HQRRP)ca_CA
dc.typeinfo:eu-repo/semantics/articleca_CA
dc.identifier.doihttps://doi.org/10.1137/16M1081270
dc.relation.projectIDThe research reported was supported by DARPA, under the contract N66001-13-1-4050, and by the NSF, under the contracts DMS-1407340, DMS-1620472, and ACI-1148125/1340293. Any opinions, ndings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily re ect the views of the National Science Foundation (NSF).ca_CA
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessca_CA
dc.relation.publisherVersionhttp://epubs.siam.org/doi/abs/10.1137/16M1081270ca_CA
dc.type.versioninfo:eu-repo/semantics/submittedVersionca_CA


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record