Anzt, Hartwig and Dongarra, Jack and Flegar, Goran and Higham, Nicholas J. and Quintana-Orti, Enrique S. (2017) Adaptive Precision in Block-Jacobi Preconditioning for Iterative Sparse Linear System Solvers. [MIMS Preprint] (In Press)
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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 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-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.
| Item Type: | MIMS Preprint |
|---|---|
| Additional Information: | To appear in Concurrency and Computation: Practice and Experience. |
| Uncontrolled Keywords: | Sparse linear systems; Krylov subspace methods; conjugate gradient (CG) method; Jacobi preconditioners; adaptive precision; communication reduction; energy efficiency |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis |
| Depositing User: | Nick Higham |
| Date Deposited: | 30 Jan 2018 09:14 |
| Last Modified: | 30 Jan 2018 09:14 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2618 |
Available Versions of this Item
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Adaptive Precision in Block-Jacobi Preconditioning for Iterative Sparse Linear System Solvers. (deposited 22 Sep 2017)
- Adaptive Precision in Block-Jacobi Preconditioning for Iterative Sparse Linear System Solvers. (deposited 30 Jan 2018 09:14) [Currently Displayed]
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