A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures
The computation of the Moore–Penrose generalized inverse is a commonly used operation in various fields such as the training of neural networks based on random weights. Therefore, a fast computation of this inverse is important for problems where such neural networks provide a solution. However, due...
- Autores:
-
Gelvez-Almeida, Elkin
Barrientos, Ricardo
Vilches, Karina
Mora, Marco
- Tipo de recurso:
- Fecha de publicación:
- 2023
- Institución:
- Universidad Simón Bolívar
- Repositorio:
- Repositorio Digital USB
- Idioma:
- eng
- OAI Identifier:
- oai:bonga.unisimon.edu.co:20.500.12442/16177
- Acceso en línea:
- https://hdl.handle.net/20.500.12442/16177
https://doi.org/10.1109/ACCESS.2023.3338544
https://ieeexplore.ieee.org/document/10336814
- Palabra clave:
- High-performance computing
Moore–Penrose generalized inverse matrix
Neural networks with random weights
Parallel computing
Strassen algorithm
- Rights
- openAccess
- License
- Attribution-NonCommercial-NoDerivs 3.0 United States
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A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures |
| title |
A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures |
| spellingShingle |
A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures High-performance computing Moore–Penrose generalized inverse matrix Neural networks with random weights Parallel computing Strassen algorithm |
| title_short |
A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures |
| title_full |
A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures |
| title_fullStr |
A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures |
| title_full_unstemmed |
A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures |
| title_sort |
A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures |
| dc.creator.fl_str_mv |
Gelvez-Almeida, Elkin Barrientos, Ricardo Vilches, Karina Mora, Marco |
| dc.contributor.author.none.fl_str_mv |
Gelvez-Almeida, Elkin Barrientos, Ricardo Vilches, Karina Mora, Marco |
| dc.subject.keywords.eng.fl_str_mv |
High-performance computing Moore–Penrose generalized inverse matrix Neural networks with random weights Parallel computing Strassen algorithm |
| topic |
High-performance computing Moore–Penrose generalized inverse matrix Neural networks with random weights Parallel computing Strassen algorithm |
| description |
The computation of the Moore–Penrose generalized inverse is a commonly used operation in various fields such as the training of neural networks based on random weights. Therefore, a fast computation of this inverse is important for problems where such neural networks provide a solution. However, due to the growth of databases, the matrices involved have large dimensions, thus requiring a significant amount of processing and execution time. In this paper, we propose a parallel computing method for the computation of the Moore–Penrose generalized inverse of large-size full-rank rectangular matrices. The proposed method employs the Strassen algorithm to compute the inverse of a nonsingular matrix and is implemented on a shared-memory architecture. The results show a significant reduction in computation time, especially for high-rank matrices. Furthermore, in a sequential computing scenario (using a single execution thread), our method achieves a reduced computation time compared with other previously reported algorithms. Consequently, our approach provides a promising solution for the efficient computation of the Moore–Penrose generalized inverse of large-size matrices employed in practical scenarios. |
| publishDate |
2023 |
| dc.date.issued.none.fl_str_mv |
2023 |
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2025-01-30T14:40:25Z |
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2025-01-30T14:40:25Z |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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info:eu-repo/semantics/article |
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Artículo científico |
| dc.identifier.citation.eng.fl_str_mv |
E. Gelvez-Almeida, R. J. Barrientos, K. Vilches-Ponce and M. Mora, "A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures," in IEEE Access, vol. 11, pp. 134834-134845, 2023, doi: 10.1109/ACCESS.2023.3338544 |
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21693536 |
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https://hdl.handle.net/20.500.12442/16177 |
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https://doi.org/10.1109/ACCESS.2023.3338544 |
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https://ieeexplore.ieee.org/document/10336814 |
| identifier_str_mv |
E. Gelvez-Almeida, R. J. Barrientos, K. Vilches-Ponce and M. Mora, "A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures," in IEEE Access, vol. 11, pp. 134834-134845, 2023, doi: 10.1109/ACCESS.2023.3338544 21693536 |
| url |
https://hdl.handle.net/20.500.12442/16177 https://doi.org/10.1109/ACCESS.2023.3338544 https://ieeexplore.ieee.org/document/10336814 |
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eng |
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eng |
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Attribution-NonCommercial-NoDerivs 3.0 United States |
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info:eu-repo/semantics/openAccess |
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openAccess |
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pdf |
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Institute of Electrical and Electronics Engineers (IEEE) |
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IEEE Access |
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Vol. 11 (2023) |
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Gelvez-Almeida, Elkinf7e2f3b2-3f16-4e8f-8009-79edc27e7a23600Barrientos, Ricardo766d5e14-34a0-49d1-a205-24903bc6bb12600Vilches, Karinabed06609-2211-4fe0-a6d5-1fed4a93d002600Mora, Marco7c36f8e4-0f3b-43d8-9735-3c7c5f71c5526002025-01-30T14:40:25Z2025-01-30T14:40:25Z2023E. Gelvez-Almeida, R. J. Barrientos, K. Vilches-Ponce and M. Mora, "A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures," in IEEE Access, vol. 11, pp. 134834-134845, 2023, doi: 10.1109/ACCESS.2023.333854421693536https://hdl.handle.net/20.500.12442/16177https://doi.org/10.1109/ACCESS.2023.3338544https://ieeexplore.ieee.org/document/10336814The computation of the Moore–Penrose generalized inverse is a commonly used operation in various fields such as the training of neural networks based on random weights. Therefore, a fast computation of this inverse is important for problems where such neural networks provide a solution. However, due to the growth of databases, the matrices involved have large dimensions, thus requiring a significant amount of processing and execution time. In this paper, we propose a parallel computing method for the computation of the Moore–Penrose generalized inverse of large-size full-rank rectangular matrices. The proposed method employs the Strassen algorithm to compute the inverse of a nonsingular matrix and is implemented on a shared-memory architecture. The results show a significant reduction in computation time, especially for high-rank matrices. Furthermore, in a sequential computing scenario (using a single execution thread), our method achieves a reduced computation time compared with other previously reported algorithms. Consequently, our approach provides a promising solution for the efficient computation of the Moore–Penrose generalized inverse of large-size matrices employed in practical scenarios.pdfengInstitute of Electrical and Electronics Engineers (IEEE)Attribution-NonCommercial-NoDerivs 3.0 United Stateshttp://creativecommons.org/licenses/by-nc-nd/3.0/us/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2IEEE AccessVol. 11 (2023)A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architecturesinfo:eu-repo/semantics/articleArtículo científicohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1High-performance computingMoore–Penrose generalized inverse matrixNeural networks with random weightsParallel computingStrassen algorithmJ. C. A. Barata and M. S. Hussein, "The Moore–Penrose pseudoinverse: A tutorial review of the theory", Brazilian J. 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Katsikis, " Further efficient hyperpower iterative methods for the computation of generalized inverses A T S ( 2) ", Revista de la Real Academia de Ciencias Exactas Físicas y Naturales. Serie A. Matemáticas, vol. 113, no. 4, pp. 3323-3339, May 2019P. S. Stanimirović, V. N. Katsikis and D. Kolundžija, "Inversion and pseudoinversion of block arrowhead matrices", Appl. Math. Comput., vol. 341, pp. 379-401, Jan. 2019.P. S. Stanimirović, F. Roy, D. K. Gupta and S. Srivastava, "Computing the Moore–Penrose inverse using its error bounds", Appl. Math. Comput., vol. 371, Apr. 2020.X. Chen and J. Ji, "A divide-and-conquer approach for the computation of the Moore–Penrose inverses", Appl. Math. Comput., vol. 379, Aug. 2020.N. Aldhafeeri, D. Pappas, I. P. Stanimirović and M. Tasić, "Representations of generalized inverses via full-rank QDR decomposition", Numer. Algorithms, vol. 86, no. 3, pp. 1327-1337, Mar. 2021.A. Ben-Israel and T. N. E. 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