2024-03-29T05:55:19Zhttps://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/1719202023-09-20T11:20:32Zcom_10234_7036com_10234_9col_10234_8620
00925njm 22002777a 4500
dc
MARTINSSON, GUNNAR
author
Quintana-Ortí, Gregorio
author
Heavner, Nathan
author
Van de Geijn, Robert A.
author
2017
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.
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.
1064-8275
1095-7197
http://hdl.handle.net/10234/171920
https://doi.org/10.1137/16M1081270
Householder QR Factorization With Randomization for Column Pivoting (HQRRP)