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A Scalable High Performant Cholesky Factorization for Multicore with GPU Accelerators

Hatem Ltaief, Stanimire Tomov, Rajib Nath, Peng Du and Jack Dongarra
Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville
High Performance Computing for Computational Science – VECPAR 2010, Lecture Notes in Computer Science, 2011, Volume 6449/2011, 93-101

@article{ltaief2011scalable,

   title={A scalable high performant Cholesky factorization for multicore with GPU accelerators},

   author={Ltaief, H. and Tomov, S. and Nath, R. and Du, P. and Dongarra, J.},

   journal={High Performance Computing for Computational Science–VECPAR 2010},

   pages={93–101},

   year={2011},

   publisher={Springer}

}

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We present a Cholesky factorization for multicore with GPU accelerators systems. The challenges in developing scalable high performance algorithms for these emerging systems stem from their heterogeneity, massive parallelism, and the huge gap between the GPUs’ compute power vs the CPU-GPU communication speed. We show an approach that is largely based on software infrastructures that have already been developed for homogeneous multicores and hybrid GPU-based computing. This results in a scalable hybrid Cholesky factorization of unprecedented performance. In particular, using NVIDIA’s Tesla S1070 (4 C1060 GPUs, each with 30 cores @1.44 GHz) connected to two dual-core AMD Opteron @1.8GHz processors, we reach up to 1.163 TFlop/s in single and up to 275 GFlop/s in double precision arithmetic. Compared with the performance of the embarrassingly parallel xGEMM over four GPUs, where no communication between GPUs are involved, our algorithm still runs at 73% and 84% for single and double precision arithmetic respectively.
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