LU factorization for accelerator-based systems

Handle URI:
http://hdl.handle.net/10754/575804
Title:
LU factorization for accelerator-based systems
Authors:
Agullo, Emmanuel; Augonnet, Cédric; Dongarra, Jack; Faverge, Mathieu; Langou, Julien; Ltaief, Hatem ( 0000-0002-6897-1095 ) ; Tomov, Stanimire Z.
Abstract:
Multicore architectures enhanced with multiple GPUs are likely to become mainstream High Performance Computing (HPC) platforms in a near future. In this paper, we present the design and implementation of an LU factorization using tile algorithm that can fully exploit the potential of such platforms in spite of their complexity. We use a methodology derived from previous work on Cholesky and QR factorizations. Our contributions essentially consist of providing new CPU/GPU hybrid LU kernels, studying the impact on performance of the looking variants as well as the storage layout in presence of pivoting, tuning the kernels for two different machines composed of multiple recent NVIDIA Tesla S1070 (four GPUs total) and Fermi-based S2050 GPUs (three GPUs total), respectively. The hybrid tile LU asymptotically achieves 1 Tflop/s in single precision on both hardwares. The performance in double precision arithmetic reaches 500 Gflop/s on the Fermi-based system, twice faster than the old GPU generation of Tesla S1070. We also discuss the impact of the number of tiles on the numerical stability. We show that the numerical results of the tile LU factorization will be accurate enough for most applications as long as the computations are performed in double precision arithmetic. © 2011 IEEE.
KAUST Department:
KAUST Supercomputing Laboratory (KSL); Extreme Computing Research Center
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2011 9th IEEE/ACS International Conference on Computer Systems and Applications (AICCSA)
Conference/Event name:
9th ACS/IEEE International Conference on Computer Systems and Applications, AICCSA 2011
Issue Date:
Dec-2011
DOI:
10.1109/AICCSA.2011.6126599
Type:
Conference Paper
ISSN:
21615322
ISBN:
9781457704741
Appears in Collections:
Conference Papers; KAUST Supercomputing Laboratory (KSL); Extreme Computing Research Center; Extreme Computing Research Center

Full metadata record

DC FieldValue Language
dc.contributor.authorAgullo, Emmanuelen
dc.contributor.authorAugonnet, Cédricen
dc.contributor.authorDongarra, Jacken
dc.contributor.authorFaverge, Mathieuen
dc.contributor.authorLangou, Julienen
dc.contributor.authorLtaief, Hatemen
dc.contributor.authorTomov, Stanimire Z.en
dc.date.accessioned2015-08-24T09:26:38Zen
dc.date.available2015-08-24T09:26:38Zen
dc.date.issued2011-12en
dc.identifier.isbn9781457704741en
dc.identifier.issn21615322en
dc.identifier.doi10.1109/AICCSA.2011.6126599en
dc.identifier.urihttp://hdl.handle.net/10754/575804en
dc.description.abstractMulticore architectures enhanced with multiple GPUs are likely to become mainstream High Performance Computing (HPC) platforms in a near future. In this paper, we present the design and implementation of an LU factorization using tile algorithm that can fully exploit the potential of such platforms in spite of their complexity. We use a methodology derived from previous work on Cholesky and QR factorizations. Our contributions essentially consist of providing new CPU/GPU hybrid LU kernels, studying the impact on performance of the looking variants as well as the storage layout in presence of pivoting, tuning the kernels for two different machines composed of multiple recent NVIDIA Tesla S1070 (four GPUs total) and Fermi-based S2050 GPUs (three GPUs total), respectively. The hybrid tile LU asymptotically achieves 1 Tflop/s in single precision on both hardwares. The performance in double precision arithmetic reaches 500 Gflop/s on the Fermi-based system, twice faster than the old GPU generation of Tesla S1070. We also discuss the impact of the number of tiles on the numerical stability. We show that the numerical results of the tile LU factorization will be accurate enough for most applications as long as the computations are performed in double precision arithmetic. © 2011 IEEE.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.subjectDense Linear Algebraen
dc.subjectHigh Performance Computingen
dc.subjectHybrid Architectureen
dc.subjectLU Factorizationen
dc.subjectMulticoreen
dc.subjectMultiple GPU Acceleratorsen
dc.subjectNumerical Accuracyen
dc.subjectTile Algorithmen
dc.titleLU factorization for accelerator-based systemsen
dc.typeConference Paperen
dc.contributor.departmentKAUST Supercomputing Laboratory (KSL)en
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journal2011 9th IEEE/ACS International Conference on Computer Systems and Applications (AICCSA)en
dc.conference.date27 December 2011 through 30 December 2011en
dc.conference.name9th ACS/IEEE International Conference on Computer Systems and Applications, AICCSA 2011en
dc.conference.locationSharm El-Sheikhen
dc.contributor.institutionINRIA, LaBRI, University of Bordeaux, Franceen
dc.contributor.institutionInnovative Computing Laboratory, University of Tennessee, Knoxville, TN 37996, United Statesen
dc.contributor.institutionUniversity of Colorado, Denver, CO 80202, United Statesen
kaust.authorLtaief, Hatemen
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