Publication
Title
Analyzing the effect of local rounding error propagation on the maximal attainable accuracy of the pipelined conjugate gradient method
Author
Abstract
Pipelined Krylov subspace methods typically offer improved strong scaling on parallel HPC hardware compared to standard Krylov subspace methods for large and sparse linear systems. In pipelined methods the traditional synchronization bottleneck is mitigated by overlapping time-consuming global communications with useful computations. However, to achieve this communication-hiding strategy, pipelined methods introduce additional recurrence relations for a number of auxiliary variables that are required to update the approximate solution. This paper aims at studying the influence of local rounding errors that are introduced by the additional recurrences in the pipelined Conjugate Gradient (CG) method. Specifically, we analyze the impact of local round-off effects on the attainable accuracy of the pipelined CG algorithm and compare it to the traditional CG method. Furthermore, we estimate the gap between the true residual and the recursively computed residual used in the algorithm. Based on this estimate we suggest an automated residual replacement strategy to reduce the loss of attainable accuracy on the final iterative solution. The resulting pipelined CG method with residual replacement improves the maximal attainable accuracy of pipelined CG while maintaining the efficient parallel performance of the pipelined method. This conclusion is substantiated by numerical results for a variety of benchmark problems.
Language
English
Source (journal)
SIAM journal on matrix analysis and applications / Society for Industrial and Applied Mathematics [Philadelphia, Pa] - Philadelphia, Pa
Publication
Philadelphia, Pa : 2018
ISSN
0895-4798
Volume/pages
39 :1 (2018) , p. 426-450
ISI
000428949900019
Full text (Publisher's DOI)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 04.05.2018
Last edited 20.09.2021
To cite this reference