Adaptive precision in block-Jacobi preconditioning for iterative sparse linear system solvers

Hartwig Anzt, Jack Dongarra, Goran Flegar, Nicholas J. Higham, Enrique S. Quintana-Ortí
2018 Concurrency and Computation  
Dongarra, J.; Higham, NJ.; Quintana Ortí, ES. (2019) . Adaptive precision in block-Jacobi preconditioning for iterative sparse linear system solvers. Concurrency and Computation Practice and Experience. 31(6):1-12. SUMMARY 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
more » ... h 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.
doi:10.1002/cpe.4460 fatcat:vkh3zx2l75bbvpvnjakollnowu