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randUTV: A Blocked Randomized Algorithm for Computing a Rank-Revealing UTV Factorization
dc.contributor.author | MARTINSSON, GUNNAR | |
dc.contributor.author | Quintana-Ortí, Gregorio | |
dc.contributor.author | Heavner, Nathan | |
dc.date.accessioned | 2019-09-11T06:59:28Z | |
dc.date.available | 2019-09-11T06:59:28Z | |
dc.date.issued | 2019-03 | |
dc.identifier.citation | MARTINSSON, Per-Gunnar; QUINTANA-ORTI, Gregorio; HEAVNER, Nathan. randUTV: A blocked randomized algorithm for computing a rank-revealing UTV factorization. ACM Transactions on Mathematical Software, 2019, vol. 45, no 1 | ca_CA |
dc.identifier.issn | 0098-3500 | |
dc.identifier.issn | 1557-7295 | |
dc.identifier.uri | http://hdl.handle.net/10234/183711 | |
dc.description.abstract | A randomized algorithm for computing a so-called UTV factorization efficiently is presented. Given a matrix , the algorithm “randUTV” computes a factorization , where and have orthonormal columns, and is triangular (either upper or lower, whichever is preferred). The algorithm randUTV is developed primarily to be a fast and easily parallelized alternative to algorithms for computing the Singular Value Decomposition (SVD). randUTV provides accuracy very close to that of the SVD for problems such as low-rank approximation, solving ill-conditioned linear systems, and determining bases for various subspaces associated with the matrix. Moreover, randUTV produces highly accurate approximations to the singular values of . Unlike the SVD, the randomized algorithm proposed builds a UTV factorization in an incremental, single-stage, and noniterative way, making it possible to halt the factorization process once a specified tolerance has been met. Numerical experiments comparing the accuracy and speed of randUTV to the SVD are presented. Other experiments also demonstrate that in comparison to column-pivoted QR, which is another factorization that is often used as a relatively economic alternative to the SVD, randUTV compares favorably in terms of speed while providing far higher accuracy. | ca_CA |
dc.format.extent | 26 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Association for Computing Machinery | ca_CA |
dc.relation.isPartOf | ACM Transactions on Mathematical Software, 2019, vol. 45, no 1 | ca_CA |
dc.rights | © Association for Computing Machinery | ca_CA |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | * |
dc.subject | numerical linear algebra | ca_CA |
dc.subject | rank-revealing matrix factorization | ca_CA |
dc.subject | singular value decomposition | ca_CA |
dc.subject | high performance | ca_CA |
dc.subject | randomized methods | ca_CA |
dc.subject | mathematics of computing | ca_CA |
dc.subject | mathematical software performance | ca_CA |
dc.subject | computations on matrices | ca_CA |
dc.title | randUTV: A Blocked Randomized Algorithm for Computing a Rank-Revealing UTV Factorization | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.1145/3242670 | |
dc.relation.projectID | DARPA: N6600-13-1-4050; NSF: DMS-1407340; DMS-1620472 | ca_CA |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | https://dl.acm.org/citation.cfm?id=3242670 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | ca_CA |
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