Adaptive precision in block‐Jacobi preconditioning for iterative sparse linear system solvers
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Other documents of the author: Anzt, Hartwig; Dongarra, Jack; Flegar, Goran; Higham, Nicholas J.; Quintana-Orti, Enrique S.
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comunitat-uji-handle2:10234/7036
comunitat-uji-handle3:10234/8620
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Title
Adaptive precision in block‐Jacobi preconditioning for iterative sparse linear system solversAuthor (s)
Date
2019-03-25Publisher
WileyISSN
1532-0626; 1532-0634Bibliographic citation
ANZT, Hartwig, et al. Adaptive precision in block‐Jacobi preconditioning for iterative sparse linear system solvers. Concurrency and Computation: Practice and Experience, 2019, vol. 31, no 6, p. e4460Type
info:eu-repo/semantics/articlePublisher version
https://onlinelibrary.wiley.com/doi/full/10.1002/cpe.4460Version
info:eu-repo/semantics/submittedVersionSubject
Abstract
We propose an adaptive scheme to reduce communication overhead caused by data movement by selectively storing the diagonal blocks of a block‐Jacobi preconditioner in different precision formats (half, single, or ... [+]
We propose an adaptive scheme to reduce communication overhead caused by data movement by selectively storing the diagonal blocks of a block‐Jacobi preconditioner in different precision formats (half, single, or double). This specialized preconditioner can then be combined with any Krylov subspace method for the solution of sparse linear systems to perform all arithmetic in double precision. We assess the effects of the adaptive precision preconditioner on the iteration count and data transfer cost of a preconditioned conjugate gradient solver. A preconditioned conjugate gradient method is, in general, a memory bandwidth‐bound algorithm, and therefore its execution time and energy consumption are largely dominated by the costs of accessing the problem's data in memory. Given this observation, we propose a model that quantifies the time and energy savings of our approach based on the assumption that these two costs depend linearly on the bit length of a floating point number. Furthermore, we use a number of test problems from the SuiteSparse matrix collection to estimate the potential benefits of the adaptive block‐Jacobi preconditioning scheme. [-]
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This is the pre-peer reviewed version of the following article: Adaptive precision in block‐Jacobi preconditioning for iterative sparse linear system solvers, which has been published in final form at https://doi.or ... [+]
This is the pre-peer reviewed version of the following article: Adaptive precision in block‐Jacobi preconditioning for iterative sparse linear system solvers, which has been published in final form at https://doi.org/10.1002/cpe.4460. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. [-]
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Concurrency and Computation: Practice and Experience, 2019, vol. 31, no 6Investigation project
Impuls und Vernetzungsfond of the Helmholtz Association. Grant Number: VH‐NG‐1241; MINECO and FEDER. Grant Number: TIN2014‐53495‐R; H2020 EU FETHPC Project. Grant Number: 732631; MathWorks; Engineering and Physical Sciences Research Council. Grant Number: EP/P020720/1; Exascale Computing Project. Grant Number: 17-SC-20-SCRights
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