Computing the Moore-Penrose inverse using its error bounds

Stanimirović, Predrag S.; Roy, Falguni; Gupta, Dharmendra K.; Srivastava, Shwetabh

doi:10.1016/j.amc.2019.124957

Cited by 4 publications

(4 citation statements)

References 19 publications

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“…Their results showed significant advantages when GPUs are employed for large-size matrix computations. Similarly, Ma et al [17], Stanimirovć et al [18]- [20],…”

Section: Introductionmentioning

confidence: 87%

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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“…Their results showed significant advantages when GPUs are employed for large-size matrix computations. Similarly, Ma et al [17], Stanimirovć et al [18]- [20],…”

Section: Introductionmentioning

confidence: 87%

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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“…Since (11) is actually another form of ( 8), the ZNN24I model ( 11) also converges to the TS u * (t) when t → ∞. According to (10), the TS of the time-varying {2,4}-inverse is the last 2mn components of u * (t). The proof is thus completed.…”

Section: Design Of a Znn Model For Computing Time-varying {24}-inversesmentioning

confidence: 99%

“…Usually, the MPI is computed using the singular value decomposition method [7,8]. However, over the last decades, a variety of methods for computing the MPI have been developed, such as in [9,10]. Fast computation algorithms are proposed for the calculation of the MPI in [9] for singular square matrices and rectangular matrices, whereas an error-bounds method that is applicable without restrictions on the rank of the matrix is presented in [10] for the calculation of the MPI of an arbitrary rectangular or singular complex matrix.…”

Section: Introductionmentioning

confidence: 99%

Computation of Time-Varying {2,3}- and {2,4}-Inverses through Zeroing Neural Networks

Lin

Simos

et al. 2022

Mathematics

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This paper investigates the problem of computing the time-varying {2,3}- and {2,4}-inverses through the zeroing neural network (ZNN) method, which is presently regarded as a state-of-the-art method for computing the time-varying matrix Moore–Penrose inverse. As a result, two new ZNN models, dubbed ZNN23I and ZNN24I, for the computation of the time-varying {2,3}- and {2,4}-inverses, respectively, are introduced, and the effectiveness of these models is evaluated. Numerical experiments investigate and confirm the efficiency of the proposed ZNN models for computing the time-varying {2,3}- and {2,4}-inverses.

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“…The importance of the MP inverse has sparked the interest of numerous scholars, leading to the development of various methods for its computation [8]- [10]. For instance, Stanimirovic et al [9] proposed an iterative scheme based on error bounds to compute the MP inverse, while Zontini et al [10] employed the generalized Schulz iterative method. However, iterative methods with a time complexity of O(n 3 ) are not suitable for handling large-scale data.…”

Section: Introductionmentioning

confidence: 99%

Efficient Predefined-Time Adaptive Neural Networks for Computing Time-Varying Tensor Moore–Penrose Inverse

Qi,

Ning,

Xiao

et al. 2024

IEEE Trans. Neural Netw. Learning Syst.

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This paper proposes predefined-time adaptive neural network (PTANN) and event-triggered PTANN (ET-PTANN) models to efficiently compute time-varying tensor Moore-Penrose inverse. The PTANN model incorporates a novel adaptive parameter and activation function, enabling it to achieve strongly predefined-time convergence. Unlike traditional time-varying parameters that increase over time, the adaptive parameter is proportional to the error norm, thereby better allocating computational resources and improving efficiency. To further enhance efficiency, the ET-PTANN model combines an event trigger with the evolution formula, resulting in the adjustment of step size and reduction of computation frequency compared to the PTANN model. By conducting mathematical derivations, the paper derives the upper bound of convergence time for the proposed neural network models and determines the minimum execution interval for the event trigger. A simulation example demonstrates that the PTANN and ET-PTANN models outperform other related neural network models in terms of computational efficiency and convergence rate. Finally, the practicality of the PTANN and ET-PTANN models is demonstrated through their application to mobile sound source localization.

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Computing the Moore-Penrose inverse using its error bounds

Cited by 4 publications

References 19 publications

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

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

Computation of Time-Varying {2,3}- and {2,4}-Inverses through Zeroing Neural Networks

Efficient Predefined-Time Adaptive Neural Networks for Computing Time-Varying Tensor Moore–Penrose Inverse

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