Accelerating linear system solutions using randomization techniques
Laboratoire de Recherche en Informatique – Universite Paris-Sud 11 (LRI), Universite Paris XI – Paris Sud
inria-00593306, 2011
@techreport{BABOULIN:2011:INRIA-00593306:1,
hal_id={inria-00593306},
url={http://hal.inria.fr/inria-00593306/en/},
title={Accelerating linear system solutions using randomization techniques},
author={Baboulin, Marc and Dongarra, Jack and Herrmann, Julien and Tomov, Stanimire},
keywords={dense linear algebra; linear systems; LU factorization; randomization; multiplicative preconditioning; Graphics Processing Units},
language={Anglais},
affiliation={Laboratoire de Recherche en Informatique – Universit{‘e} Paris-Sud 11 – LRI , Innovative Computing Laboratory – ICL},
type={Rapport de recherche},
institution={INRIA},
number={RR-7616},
year={2011},
month={May},
pdf={http://hal.inria.fr/inria-00593306/PDF/RR-7616.pdf}
}
We illustrate how linear algebra calculations can be enhanced by statistical techniques in the case of a square linear system Ax = b. We study a random transformation of A that enables us to avoid pivoting and then to reduce the amount of communication. Numerical experiments show that this randomization can be performed at a very affordable computational price while providing us with a satisfying accuracy when compared to partial pivoting. This random transformation called Partial Random Butter y Transformation (PRBT) is optimized in terms of data storage and flops count. We propose a solver where PRBT and the LU factorization with no pivoting take advantage of the latest generation of hybrid multicore/GPU machines and we compare its Gfl op/s performance with a solver implemented in a current parallel library.
December 25, 2011 by hgpu
