Householder QR Factorization With Randomization for Column Pivoting (HQRRP)
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Other documents of the author: MARTINSSON, GUNNAR; Quintana-Ortí, Gregorio; Heavner, Nathan; Van de Geijn, Robert A.
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Title
Householder QR Factorization With Randomization for Column Pivoting (HQRRP)Date
2017Publisher
Society for Industrial and Applied MathematicsISSN
1064-8275; 1095-7197Bibliographic citation
Martinsson, 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.Type
info:eu-repo/semantics/articlePublisher version
http://epubs.siam.org/doi/abs/10.1137/16M1081270Version
info:eu-repo/semantics/submittedVersionAbstract
A 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 ... [+]
A 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. [-]
Is part of
SIAM Journal on Scientific Computing, 2017, vol. 39, no 2, p. C96-C115.Investigation project
The 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).Rights
http://rightsstatements.org/vocab/CNE/1.0/
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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