General framework for deriving reproducible Krylov subspace algorithms: A BiCGStab case study - Sorbonne Université Access content directly
Preprints, Working Papers, ... Year : 2021

General framework for deriving reproducible Krylov subspace algorithms: A BiCGStab case study

Abstract

Parallel implementations of Krylov subspace algorithms often help to accelerate the procedure to find the solution of a linear system. However, from the other side, such parallelization coupled with asynchronous and out-of-order execution often enlarge the non-associativity of floating-point operations. This results in non-reproducibility on the same or different settings. This paper proposes a general framework for deriving reproducible and accurate variants of a Krylov subspace algorithm. The proposed algorithmic strategies are reinforced by programmability suggestions to assure deterministic and accurate executions. The framework is illustrated on the preconditioned BiCGStab method for the solution of non-symmetric linear systems in parallel environments with message-passing. Finally, we verify the two reproducible variants of PBiCGStab on a set matrices from the SuiteSparse Matrix Collection.
Fichier principal
Vignette du fichier
PPAM___Reproducible__P_BiCGStab_Camera_ready-7.pdf (380.1 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03382119 , version 1 (18-10-2021)
hal-03382119 , version 2 (03-11-2022)

Identifiers

  • HAL Id : hal-03382119 , version 2

Cite

Roman Iakymchuk, Stef Graillat, José I Aliaga. General framework for deriving reproducible Krylov subspace algorithms: A BiCGStab case study. 2021. ⟨hal-03382119v2⟩
109 View
163 Download

Share

Gmail Facebook X LinkedIn More