LU factorization for accelerator-based systems

• Published in: 2011 9th IEEE/ACS International Conference on Computer Systems and Applications (AICCSA) pp. 217 - 224
• Main Authors: Agullo, E., Augonnet, C., Dongarra, J., Faverge, M., Langou, J., Ltaief, Hatem, Tomov, S.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2011
• Subjects: Algorithm design and analysis; Dense Linear Algebra; Graphics processing unit; High Performance Computing; Hybrid Architecture; Kernel; LU Factorization; Multicore; Multicore processing; Multiple GPU Accelerators; Numerical Accuracy; Optimization; Tile Algorithm; Tiles
• ISBN: 9781457704758; 1457704757
• ISSN: 2161-5322
• DOI: 10.1109/AICCSA.2011.6126599

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.