Calculating the Moore–Penrose Generalized Inverse on Massively Parallel Systems

Stanojević, Vukašin; Kazakovtsev, Lev; Stanimirović, Predrag S.; Rezova, Natalya; Shkaberina, Guzel

doi:10.3390/a15100348

Cited by 7 publications

(4 citation statements)

References 45 publications

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“…In this section, we introduce our parallel computing method for the computation of the Moore-Penrose generalized inverse. As mentioned in Section I, various computational methods have been developed for the computation of the Moore-Penrose generalized inverse [4], [5], [8]- [10], [16]. In this paper, we develop a parallel computing algorithm for shared-memory architectures.…”

Section: Proposed Methodsmentioning

confidence: 99%

“…More recently, Stanojevi'c et al [16] proposed an algorithm based on the generalized Cholesky factorization and the Strassen matrix inversion algorithm, which has been specifically designed for parallel computing architectures, particularly for using graphics processing units (GPUs) in the compute unified device architecture. Their results showed significant advantages when GPUs are employed for large-size matrix computations.…”

Section: Introductionmentioning

confidence: 99%

“…In turn, temporary matrix R 5 and submatrix X 11 (lines 14 and 19, respectively) are obtained using Algorithm 2. R 2 , R 3 , R 4 , X 12 , X 21 , and R 7 (lines 11,12,13,16,17, and 18, respectively) are computed using Algorithm 3. For submatrix X 22 (line 20), an approach similar to that of Algorithms 2 and 3 is employed, where each thread performs the sign change in the rows assigned by the program.…”

mentioning

confidence: 99%

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A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures

Gelvez-Almeida,

Barrientos,

Vilches-Ponce

et al. 2023

IEEE Access

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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.INDEX TERMS High-performance computing, Moore-Penrose generalized inverse matrix, neural networks with random weights, parallel computing, Strassen algorithm.

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Section: Proposed Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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A Parallel Computing Method for the Computation of the Moore–Penrose Generalized Inverse for Shared-Memory Architectures

Gelvez-Almeida,

Barrientos,

Vilches-Ponce

et al. 2023

IEEE Access

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“…If D is a (m × n) matrix, then pseudo inverse computation based on singular value decomposition is O(nmmin(m, n)) [17], [18]. The least squares estimator ( 9) can be expressed as…”

Section: Data Driven Level Set Fuzzy Modelingmentioning

confidence: 99%

Data Driven Level Set Fuzzy and Neural Modeling

Leite,

Gomide

2024

Preprint

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Data driven modeling has been a major approach for learning and understanding systems, ranging from medical, biological, environmental, meteorological, transportation, and economic systems to complex dynamic information, engineering, and hybrid systems. Computational intelligence, rooted in fuzzy systems, neural networks, evolutionary computation and their hybridizations, is a key driving force in the current data driven system modeling effort. This paper addresses data driven fuzzy modeling and neural modeling structures, and evaluates their performances in nonlinear dynamic systems modeling tasks. Data driven fuzzy modeling and neural modeling structures are powerful modeling paradigms that compete closely, often surpassing most of the alternative state of the art methods such as gradient boosting, kernel ridge regression, and Gaussian processes. In particular, the complexity and approximation capabilities of the data driven fuzzy modeling, long-short term memory, convolutional, and hybrid neural modeling structures are evaluated, and their usefulness are discussed in front of the accuracy of the predictions, and the complexity of the models they produce.

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