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 tiled WZ factorization algorithm which can fully exploit such architectures are presented. Three parallel implementations of the algorithm are...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2019-06-01
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| Series: | International Journal of Applied Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/amcs-2019-0030 |
| _version_ | 1818734912196313088 |
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| author | Bylina Beata Bylina Jarosław |
| author_facet | Bylina Beata Bylina Jarosław |
| author_sort | Bylina Beata |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-18T00:12:54Z |
| format | Article |
| id | doaj.art-819c7c2de3634a8cb687cebabdcfbbbe |
| institution | Directory Open Access Journal |
| issn | 2083-8492 |
| language | English |
| last_indexed | 2024-12-18T00:12:54Z |
| publishDate | 2019-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | International Journal of Applied Mathematics and Computer Science |
| spelling | doaj.art-819c7c2de3634a8cb687cebabdcfbbbe2022-12-21T21:27:38ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922019-06-0129240741910.2478/amcs-2019-0030amcs-2019-0030The Parallel Tiled WZ Factorization Algorithm for Multicore ArchitecturesBylina Beata0Bylina Jarosław1Institute of Mathematics, Marie Curie-Skłodowska University, Pl. M. Curie-Skłodowskiej 5, 20-031Lublin, PolandInstitute of Mathematics, Marie Curie-Skłodowska University, Pl. M. Curie-Skłodowskiej 5, 20-031Lublin, PolandThe 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.https://doi.org/10.2478/amcs-2019-0030tiled algorithmwz factorizationsolution of linear systemsamdahl’s lawhigh performance computingmulticore architectures |
| spellingShingle | Bylina Beata Bylina Jarosław The Parallel Tiled WZ Factorization Algorithm for Multicore Architectures International Journal of Applied Mathematics and Computer Science tiled algorithm wz factorization solution of linear systems amdahl’s law high performance computing multicore architectures |
| title | The Parallel Tiled WZ Factorization Algorithm for Multicore Architectures |
| title_full | The Parallel Tiled WZ Factorization Algorithm for Multicore Architectures |
| title_fullStr | The Parallel Tiled WZ Factorization Algorithm for Multicore Architectures |
| title_full_unstemmed | The Parallel Tiled WZ Factorization Algorithm for Multicore Architectures |
| title_short | The Parallel Tiled WZ Factorization Algorithm for Multicore Architectures |
| title_sort | parallel tiled wz factorization algorithm for multicore architectures |
| topic | tiled algorithm wz factorization solution of linear systems amdahl’s law high performance computing multicore architectures |
| url | https://doi.org/10.2478/amcs-2019-0030 |
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