Efficiency of General Krylov Methods on GPUs – An Experimental Study

TitleEfficiency of General Krylov Methods on GPUs – An Experimental Study
Publication TypeConference Proceedings
Year of Publication2016
AuthorsAnzt, H., J. Dongarra, M. Kreutzer, G. Wellein, and M. Kohler
Conference Name2016 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)
Date Published2016-05
Keywordsalgorithmic bombardment, BiCGSTAB, CGS, Convergence, Electric breakdown, gpu, graphics processing units, Hardware, IDR(s), Krylov solver, Libraries, linear systems, QMR, Sparse matrices
AbstractThis paper compares different Krylov methods based on short recurrences with respect to their efficiency whenimplemented on GPUs. The comparison includes BiCGSTAB, CGS, QMR, and IDR using different shadow space dimensions. These methods are known for their good convergencecharacteristics. For a large set of test matrices taken from theUniversity of Florida Matrix Collection, we evaluate the methods'performance against different target metrics: convergence, number of sparse matrix-vector multiplications, and executiontime. We also analyze whether the methods are "orthogonal"in terms of problem suitability. We propose best practicesfor choosing methods in a "black box" scenario, where noinformation about the optimal solver is available.