Analysis and performance estimation of the conjugate gradient method on multiple GPUs

Mickeal Verschoor, Andrei C. Jalba
Institute for Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 3500 MB Eindhoven, The Netherlands
Journal of Parallel Computing, 2012

   title={Analysis and performance estimation of the conjugate gradient method on multiple gpus},

   author={VERSCHOOR, M. and JALBA, AC},

   journal={Parallel Computing},



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The Conjugate Gradient (CG) method is a widely-used iterative method for solving linear systems described by a (sparse) matrix. The method requires a large amount of Sparse-Matrix Vector (SpMV) multiplications, vector reductions and other vector operations to be performed. We present a number of mappings for the SpMV operation on modern programmable GPUs using the Block Compressed Sparse Row (BCSR) format. Further, we show that reordering matrix blocks substantially improves the performance of the SpMV operation, especially when small blocks are used, so that our method outperforms existing state-of-the-art approaches, in most cases. Finally, a thorough analysis of the performance of both SpMV and CG methods is performed, which allows us to model and estimate the expected maximum performance for a given (unseen) problem.
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