Combining sparse approximate factorizations with mixed precision iterative refinement
| Autor: | Patrick Amestoy, Alfredo Buttari, Nicholas Higham, Excellent, Jean-Yves L., Théo Mary, Bastien Vieublé |
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| Přispěvatelé: | Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT), École normale supérieure de Lyon (ENS de Lyon), Mumps Technologies [Lyon], Algorithmes Parallèles et Optimisation (IRIT-APO), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Centre National de la Recherche Scientifique (CNRS), University of Manchester [Manchester], Department of Mathematics [Manchester] (School of Mathematics), Performance et Qualité des Algorithmes Numériques (PEQUAN), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Olympe supercomputer of the CALMIP center (project P0989), European Project: 676629,H2020 Pilier Excellent Science,H2020-EINFRA-2015-1,EoCoE(2015), Vieublé, Bastien, Energy oriented Centre of Excellence for computer applications - EoCoE - - H2020 Pilier Excellent Science2015-10-01 - 2018-09-30 - 676629 - VALID |
| Předmět: |
multifrontal method
parallelism mixed precision floating-point arithmetic GMRES [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA] rounding error analysis [INFO.INFO-PF]Computer Science [cs]/Performance [cs.PF] [INFO.INFO-MS] Computer Science [cs]/Mathematical Software [cs.MS] [INFO.INFO-PF] Computer Science [cs]/Performance [cs.PF] preconditioning [INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA] sparse direct solver iterative refinement linear system multiple precision [INFO.INFO-MS]Computer Science [cs]/Mathematical Software [cs.MS] |
| Zdroj: | HAL ACM Transactions on Mathematical Software ACM Transactions on Mathematical Software, In press |
| ISSN: | 0098-3500 |
| Popis: | International audience; The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so we first develop a new error analysis for LU-and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank (BLR) factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that the proposed approach can lead to considerable reductions of both the time and memory consumption. |
| Databáze: | OpenAIRE |
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