The parallel tiled WZ factorization algorithm for multicore architectures

• Autorzy: Bylina Beata , Bylina Jarosław

Identyfikatory

DOI

10.2478/amcs-2019-0030

• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to investigate dense linear algebra algorithms on shared memory multicore architectures. The design and implementation of a parallel tiled WZ factorization algorithm which can fully exploit such architectures are presented. Three parallel implementations of the algorithm are studied. The first one relies only on exploiting multithreaded BLAS (basic linear algebra subprograms) operations. The second implementation, except for BLAS operations, employs the OpenMP standard to use the loop-level parallelism. The third implementation, except for BLAS operations, employs the OpenMP task directive with the depend clause. We report the computational performance and the speedup of the parallel tiled WZ factorization algorithm on shared memory multicore architectures for dense square diagonally dominant matrices. Then we compare our parallel implementations with the respective LU factorization from a vendor implemented LAPACK library. We also analyze the numerical accuracy. Two of our implementations can be achieved with near maximal theoretical speedup implied by Amdahl’s law.

Słowa kluczowe

EN

tiled algorithm; WZ factorization; solution of linear system; Amdahl’s law; high performance computing; multicore architecture

PL

rozkład WZ; układ liniowy; prawo Amdahla; architektura wielordzeniowa

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2019
• Tom: Vol. 29, no. 2
• Strony: 407--419
• Opis fizyczny: Bibliogr. 22 poz., rys., tab., wykr.

Twórcy

autor

Bylina Beata

• Institute of Mathematics, Marie Curie-Skłodowska University, Pl. M. Curie-Skłodowskiej 5, 20-031 Lublin, Poland

autor

Bylina Jarosław

• Institute of Mathematics, Marie Curie-Skłodowska University, Pl. M. Curie-Skłodowskiej 5, 20-031 Lublin, Poland

Bibliografia

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• [8] Bylina, B. and Bylina, J. (2015). Strategies of parallelizing nested loops on the multicore architectures on the example of the WZ factorization for the dense matrices, in M. Ganzha et al. (Eds.), Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, Annals of Computer Science and Information Systems, Vol. 5, IEEE, Piscataway, NJ, pp. 629–639.
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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).