randUTV: A Blocked Randomized Algorithm for Computing a Rank-Revealing UTV Factorization
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Títol
randUTV: A Blocked Randomized Algorithm for Computing a Rank-Revealing UTV FactorizationData de publicació
2019-03Editor
Association for Computing MachineryISSN
0098-3500; 1557-7295Cita bibliogràfica
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 1Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
https://dl.acm.org/citation.cfm?id=3242670Versió
info:eu-repo/semantics/submittedVersionParaules clau / Matèries
Resum
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 ... [+]
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. [-]
Publicat a
ACM Transactions on Mathematical Software, 2019, vol. 45, no 1Proyecto de investigación
DARPA: N6600-13-1-4050; NSF: DMS-1407340; DMS-1620472Drets d'accés
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