TY - GEN
T1 - LU factorization for accelerator-based systems
AU - Agullo, Emmanuel
AU - Augonnet, Cédric
AU - Dongarra, Jack
AU - Faverge, Mathieu
AU - Langou, Julien
AU - Ltaief, Hatem
AU - Tomov, Stanimire
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - Dense Linear Algebra
KW - High Performance Computing
KW - Hybrid Architecture
KW - LU Factorization
KW - Multicore
KW - Multiple GPU Accelerators
KW - Numerical Accuracy
KW - Tile Algorithm
UR - http://www.scopus.com/inward/record.url?scp=84857696452&partnerID=8YFLogxK
U2 - 10.1109/AICCSA.2011.6126599
DO - 10.1109/AICCSA.2011.6126599
M3 - Conference contribution
AN - SCOPUS:84857696452
SN - 9781457704741
T3 - Proceedings of IEEE/ACS International Conference on Computer Systems and Applications, AICCSA
SP - 217
EP - 224
BT - Proceedings of the 2011 9th IEEE/ACS International Conference on Computer Systems and Applications, AICCSA 2011
T2 - 9th ACS/IEEE International Conference on Computer Systems and Applications, AICCSA 2011
Y2 - 27 December 2011 through 30 December 2011
ER -