<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

The Parallel Tiled WZ Factorization Algorithm for Multicore Architectures

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"The Parallel Tiled WZ Factorization Algorithm for Multicore Architectures"}

The aim of this paper is to investigate dense linear algebra algorithms on shared memory multicore architectures. The design and implementation of a parallel...

The Parallel Tiled WZ Factorization Algorithm for Multicore Architectures

Published Online: Jul 04, 2019

Page range: 407 - 419

Received: Sep 08, 2018

Accepted: Mar 02, 2019

DOI: https://doi.org/10.2478/amcs-2019-0030

Keywords
tiled algorithm, WZ factorization, solution of linear systems, Amdahl’s law, high performance computing, multicore architectures

© 2019 Beata Bylina et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The Parallel Tiled WZ Factorization Algorithm for Multicore Architectures

Published Online: Jul 04, 2019

Page range: 407 - 419

Received: Sep 08, 2018

Accepted: Mar 02, 2019

DOI: https://doi.org/10.2478/amcs-2019-0030

Keywordstiled algorithm, WZ factorization, solution of linear systems, Amdahl’s law, high performance computing, multicore architectures

© 2019 Beata Bylina et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
tiled algorithm, WZ factorization, solution of linear systems, Amdahl’s law, high performance computing, multicore architectures