A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures
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Fecha
2023
Autores
Gelvez-Almeida, Elkin
Barrientos, Ricardo
Vilches, Karina
Mora, Marco
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Institute of Electrical and Electronics Engineers (IEEE)
Resumen
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.
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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
