Premium
Adaptive precision in block‐Jacobi preconditioning for iterative sparse linear system solvers
Author(s) -
Anzt Hartwig,
Dongarra Jack,
Flegar Goran,
Higham Nicholas J.,
QuintanaOrtí Enrique S.
Publication year - 2018
Publication title -
concurrency and computation: practice and experience
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.309
H-Index - 67
eISSN - 1532-0634
pISSN - 1532-0626
DOI - 10.1002/cpe.4460
Subject(s) - preconditioner , conjugate gradient method , krylov subspace , solver , computer science , block (permutation group theory) , jacobi method , linear system , iterative method , algorithm , overhead (engineering) , sparse matrix , parallel computing , mathematical optimization , mathematics , mathematical analysis , physics , geometry , quantum mechanics , gaussian , operating system
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 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.