Efficiency of general Krylov methods on GPUs – An experimental study

Hartwig Anzt, Jack Dongarra, Moritz Kreutzer, Gerhard Wellein, Martin Kohler
University of Tennessee, Knoxville, TN, USA
The Sixth International Workshop on Accelerators and Hybrid Exascale Systems (AsHES), 2016


   title={Efficiency of general Krylov methods on GPUs–An experimental study},

   author={Anzt, Hartwig and Dongarra, Jack and Kreutzer, Moritz and Wellein, Gerhard and K{"o}hler, Martin},



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This paper compares different Krylov methods based on short recurrences with respect to their efficiency when implemented on GPUs. The comparison includes BiCGSTAB, CGS, QMR, and IDR using different shadow space dimensions. These methods are known for their good convergence characteristics. For a large set of test matrices taken from the University of Florida Matrix Collection, we evaluate the methods’ performance against different target metrics: convergence, number of sparse matrix-vector multiplications, and execution time. We also analyze whether the methods are "orthogonal" in terms of problem suitability. We propose best practices for choosing methods in a "black box" scenario, where no information about the optimal solver is available.
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