8530

A scalable, numerically stable, high-performance tridiagonal solver using GPUs

Li-Wen Chang, John A. Stratton, Hee-Seok Kim, Wen-Mei W. Hwu
Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
International Conference on High Performance Computing, Networking, Storage and Analysis (SC’12), 2012

@inproceedings{chang2012scalable,

   title={A scalable, numerically stable, high-performance tridiagonal solver using GPUs},

   author={Chang, L.W. and Stratton, J.A. and Kim, H.S. and Hwu, W.M.W.},

   booktitle={Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis},

   pages={27},

   year={2012},

   organization={IEEE Computer Society Press}

}

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In this paper, we present a scalable, numerically stable, high-performance tridiagonal solver. The solver is based on the SPIKE algorithm for partitioning a large matrix into small independent matrices, which can be solved in parallel. For each small matrix, our solver applies a general 1-by-1 or 2-by-2 diagonal pivoting algorithm, which is also known to be numerically stable. Our paper makes two major contributions. First, our solver is the first numerically stable tridiagonal solver for GPUs. Our solver provides comparable quality of stable solutions to Intel MKL and Matlab, at speed comparable to the GPU tridiagonal solvers in existing packages like CUSPARSE. It is also scalable to multiple GPUs and CPUs. Second, we present and analyze two key optimization strategies for our solver: a high-throughput data layout transformation for memory efficiency, and a dynamic tiling approach for reducing the memory access footprint caused by branch divergence.
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