General Framework for Deriving Reproducible Krylov Subspace Algorithms: BiCGStab Case
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Other documents of the author: Iakymchuk, Roman; Graillat, Stef; Aliaga Estellés, José Ignacio
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Title
General Framework for Deriving Reproducible Krylov Subspace Algorithms: BiCGStab CaseDate
2023Publisher
SpringerISBN
978-3-031-30441-5; 978-3-031-30442-2Bibliographic citation
IAKYMCHUK, Roman; GRAILLAT, Stef; ALIAGA, José I. General Framework for Deriving Reproducible Krylov Subspace Algorithms: BiCGStab Case. En International Conference on Parallel Processing and Applied Mathematics. Cham: Springer International Publishing, 2022. p. 16-29.Type
info:eu-repo/semantics/bookPartPublisher version
https://link.springer.com/chapter/10.1007/978-3-031-30442-2_2Version
info:eu-repo/semantics/acceptedVersionSubject
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 ... [+]
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 with message-passing. Finally,
we verify the two reproducible variants of PBiCGStab on a set matrices
from the SuiteSparse Matrix Collection and a 3D Poisson’s equation. [-]
Is part of
International Conference on Parallel Processing and Applied MathematicsFunder Name
Agencia Estatal de Investigación | European Union’s Horizon 2020
Project code
PID2020- 113656RB-C21 | MCIN/AEI/10.13039/501100011033 | ANR-20-CE46-0009 | info:eu-repo/grantAgreement/EC/H2020/842528
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© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
R. Wyrzykowski et al. (Eds.): PPAM 2022, LNCS 13826, pp. 16–29, 2023.
https://doi.org/10.1007/978-3-031-30442-2_2
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