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Iakymchuk, Roman
Publications (2 of 2) Show all publications
Iakymchuk, R., Graillat, S. & Aliaga, J. I. (2023). General framework for re-assuring numerical reliability in parallel Krylov solvers: a case of bi-conjugate gradient stabilized methods. The international journal of high performance computing applications
Open this publication in new window or tab >>General framework for re-assuring numerical reliability in parallel Krylov solvers: a case of bi-conjugate gradient stabilized methods
2023 (English)In: The international journal of high performance computing applications, ISSN 1094-3420, E-ISSN 1741-2846Article in journal (Refereed) Epub ahead of print
Abstract [en]

Parallel implementations of Krylov subspace methods often help to accelerate the procedure of finding an approximate solution of a linear system. However, such parallelization coupled with asynchronous and out-of-order execution often makes more visible the non-associativity impact in floating-point operations. These problems are even amplified when communication-hiding pipelined algorithms are used to improve the parallelization of Krylov subspace methods. Introducing reproducibility in the implementations avoids these problems by getting more robust and correct solutions. This paper proposes a general framework for deriving reproducible and accurate variants of Krylov subspace methods. The proposed algorithmic strategies are reinforced by programmability suggestions to assure deterministic and accurate executions. The framework is illustrated on the preconditioned BiCGStab method and its pipelined modification, which in fact is a distinctive method from the Krylov subspace family, for the solution of non-symmetric linear systems with message-passing. Finally, we verify the numerical behavior of the two reproducible variants of BiCGStab on a set of matrices from the SuiteSparse Matrix Collection and a 3D Poisson’s equation.

Place, publisher, year, edition, pages
Sage Publications, 2023
Keywords
accuracy, ExBLAS, HPC, Numerical reliability, PBiCGStab, pipelined PBiCGStab, reproducibility
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-216137 (URN)10.1177/10943420231207642 (DOI)2-s2.0-85174938956 (Scopus ID)
Available from: 2023-11-02 Created: 2023-11-02 Last updated: 2023-11-02
Iakymchuk, R., Graillat, S. & Aliaga, J. I. (2023). General framework for deriving reproducible krylov subspace algorithms: BiCGStab case. In: Roman Wyrzykowski; Jack Dongarra; Ewa Deelman; Konrad Karczewski (Ed.), Parallel processing and applied mathematics: 14th International Conference, PPAM 2022, Gdansk, Poland, September 11–14, 2022, Revised Selected Papers, Part I. Paper presented at 14th International Conference on Parallel Processing and Applied Mathematics, PPAM 2022, September 11-14, 2022. (pp. 16-29). Springer Science+Business Media B.V.
Open this publication in new window or tab >>General framework for deriving reproducible krylov subspace algorithms: BiCGStab case
2023 (English)In: Parallel processing and applied mathematics: 14th International Conference, PPAM 2022, Gdansk, Poland, September 11–14, 2022, Revised Selected Papers, Part I / [ed] Roman Wyrzykowski; Jack Dongarra; Ewa Deelman; Konrad Karczewski, Springer Science+Business Media B.V., 2023, p. 16-29Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer Science+Business Media B.V., 2023
Series
Lecture Notes in Computer Science, ISSN 03029743, E-ISSN 16113349 ; 13826
Keywords
accuracy, floating-point expansion, fused multiply-add, long accumulator, preconditioned BiCGStab, Reproducibility
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:umu:diva-210209 (URN)10.1007/978-3-031-30442-2_2 (DOI)2-s2.0-85161362443 (Scopus ID)9783031304415 (ISBN)978-3-031-30442-2 (ISBN)
Conference
14th International Conference on Parallel Processing and Applied Mathematics, PPAM 2022, September 11-14, 2022.
Available from: 2023-06-28 Created: 2023-06-28 Last updated: 2023-06-28Bibliographically approved
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