A Class of Communication-avoiding Algorithms for Solving General Dense Linear Systems on CPU/GPU Parallel Machines
We study several solvers for the solution of general linear systems where the main objective is to reduce the communication overhead due to pivoting. We first describe two existing algorithms for the LU factorization on hybrid CPU/GPU architectures. The first one is based on partial pivoting and the...
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| Published in: | Procedia computer science Vol. 9; pp. 17 - 26 |
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| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
2012
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| ISSN: | 1877-0509, 1877-0509 |
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| Abstract | We study several solvers for the solution of general linear systems where the main objective is to reduce the communication overhead due to pivoting. We first describe two existing algorithms for the LU factorization on hybrid CPU/GPU architectures. The first one is based on partial pivoting and the second uses a random preconditioning of the original matrix to avoid pivoting. Then we introduce a solver where the panel factorization is performed using a communication-avoiding pivoting heuristic while the update of the trailing submatrix is performed by the GPU. We provide performance comparisons and tests on accuracy for these solvers on current hybrid multicore-GPU parallel machines. |
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| AbstractList | We study several solvers for the solution of general linear systems where the main objective is to reduce the communication overhead due to pivoting. We first describe two existing algorithms for the LU factorization on hybrid CPU/GPU architectures. The first one is based on partial pivoting and the second uses a random preconditioning of the original matrix to avoid pivoting. Then we introduce a solver where the panel factorization is performed using a communication-avoiding pivoting heuristic while the update of the trailing submatrix is performed by the GPU. We provide performance comparisons and tests on accuracy for these solvers on current hybrid multicore-GPU parallel machines. |
| Author | Baboulin, Marc Rémy, Adrien Dongarra, Jack Grigori, Laura Donfack, Simplice Tomov, Stanimire |
| Author_xml | – sequence: 1 givenname: Marc surname: Baboulin fullname: Baboulin, Marc email: marc.baboulin@inria.fr organization: Inria and University Paris-Sud, France – sequence: 2 givenname: Simplice surname: Donfack fullname: Donfack, Simplice email: simplice.donfack@lri.fr organization: Inria and University Paris-Sud, France – sequence: 3 givenname: Jack surname: Dongarra fullname: Dongarra, Jack email: dongarra@eecs.utk.edu organization: University of Tennessee, USA – sequence: 4 givenname: Laura surname: Grigori fullname: Grigori, Laura email: laura.grigori@inria.fr organization: Inria and University Paris-Sud, France – sequence: 5 givenname: Adrien surname: Rémy fullname: Rémy, Adrien email: adrien.remy@lri.fr organization: Inria and University Paris-Sud, France – sequence: 6 givenname: Stanimire surname: Tomov fullname: Tomov, Stanimire email: tomov@eecs.utk.edu organization: University of Tennessee, USA |
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| Cites_doi | 10.1177/1094342010385729 10.1016/j.parco.2009.12.005 10.1016/j.parco.2010.06.001 10.1137/1.9780898718027 10.1109/SC.2008.5214287 10.1090/S0025-5718-1980-0572859-4 10.1137/100788926 10.1002/cpe.1301 10.1137/1.9780898719642 10.1007/3-540-60902-4_13 10.1137/1.9781611971811 10.1137/1.9780898719604 10.1147/rd.416.0737 10.1109/IPDPS.2011.15 10.1109/IPDPS.2010.5470348 10.1137/1.9780898719611 |
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| Keywords | linear system solvers dense linear algebra libraries LU factorization communication-avoiding algorithms hybrid multicore/GPU computing |
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Exper. doi: 10.1002/cpe.1301 – ident: 10.1016/j.procs.2012.04.003_bib0045 – ident: 10.1016/j.procs.2012.04.003_bib0015 doi: 10.1137/1.9780898719642 – ident: 10.1016/j.procs.2012.04.003_bib0020 doi: 10.1007/3-540-60902-4_13 – ident: 10.1016/j.procs.2012.04.003_bib0095 – ident: 10.1016/j.procs.2012.04.003_bib0105 – ident: 10.1016/j.procs.2012.04.003_bib0005 doi: 10.1137/1.9781611971811 – ident: 10.1016/j.procs.2012.04.003_bib0010 doi: 10.1137/1.9780898719604 – volume: 41 start-page: 737 issue: 6 year: 1997 ident: 10.1016/j.procs.2012.04.003_bib0100 article-title: Recursion leads to automatic variable blocking for dense linear-algebra algorithms publication-title: IBM Journal of Research and Development doi: 10.1147/rd.416.0737 – ident: 10.1016/j.procs.2012.04.003_bib0040 doi: 10.1109/IPDPS.2011.15 – ident: 10.1016/j.procs.2012.04.003_bib0080 doi: 10.1109/IPDPS.2010.5470348 – ident: 10.1016/j.procs.2012.04.003_bib0110 – ident: 10.1016/j.procs.2012.04.003_bib0070 doi: 10.1137/1.9780898719611 – ident: 10.1016/j.procs.2012.04.003_bib0075 |
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| SubjectTerms | communication-avoiding algorithms dense linear algebra libraries hybrid multicore/GPU computing linear system solvers LU factorization |
| Title | A Class of Communication-avoiding Algorithms for Solving General Dense Linear Systems on CPU/GPU Parallel Machines |
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