An efficient second‐order neural network model for computing the Moore–Penrose inverse of matrices

Abstract The computation of the Moore–Penrose inverse is widely encountered in science and engineering. Due to the parallel‐processing nature and strong‐learning ability, the neural network has become a promising approach to solving the Moore–Penrose inverse recently. However, almost all the existin...

Full description

Saved in:
Bibliographic Details
Main Authors: Lin Li, Jianhao Hu
Format: Article
Language:English
Published: Wiley 2022-12-01
Series:IET Signal Processing
Subjects:
Online Access:https://doi.org/10.1049/sil2.12156
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850110181812207616
author Lin Li
Jianhao Hu
author_facet Lin Li
Jianhao Hu
author_sort Lin Li
collection DOAJ
description Abstract The computation of the Moore–Penrose inverse is widely encountered in science and engineering. Due to the parallel‐processing nature and strong‐learning ability, the neural network has become a promising approach to solving the Moore–Penrose inverse recently. However, almost all the existing neural networks for matrix inversion are based on the gradient‐descent (GD) method, whose main drawbacks are slow convergence and sensitivity to learning parameters. Moreover, there is no unified neural network to compute the Moore–Penrose inverse for both the full‐rank matrix and rank‐deficient matrix. In this paper, an efficient second‐order neural network model with the improved Newton's method is proposed to obtain the accurate Moore–Penrose inverse of an arbitrary matrix by one epoch without any learning parameter. Compared with the GD‐based neural networks for Moore–Penrose inverse computation, the proposed model converges faster and has lower complexity. Furthermore, through in‐depth derivation, the neural network for computing the Moore–Penrose inverse is well interpretable. Numerical studies and application to the random matrix inversion in multiple‐input multiple‐output detection are provided to validate the efficiency of the proposed model for solving the Moore–Penrose inverse.
format Article
id doaj-art-47bdbadd8b1b4e5ca8ae792dbbd9e844
institution OA Journals
issn 1751-9675
1751-9683
language English
publishDate 2022-12-01
publisher Wiley
record_format Article
series IET Signal Processing
spelling doaj-art-47bdbadd8b1b4e5ca8ae792dbbd9e8442025-08-20T02:37:53ZengWileyIET Signal Processing1751-96751751-96832022-12-011691106111710.1049/sil2.12156An efficient second‐order neural network model for computing the Moore–Penrose inverse of matricesLin Li0Jianhao Hu1National Key Laboratory of Science and Technology on Communications University of Electronic Science and Technology of China Sichuan ChinaNational Key Laboratory of Science and Technology on Communications University of Electronic Science and Technology of China Sichuan ChinaAbstract The computation of the Moore–Penrose inverse is widely encountered in science and engineering. Due to the parallel‐processing nature and strong‐learning ability, the neural network has become a promising approach to solving the Moore–Penrose inverse recently. However, almost all the existing neural networks for matrix inversion are based on the gradient‐descent (GD) method, whose main drawbacks are slow convergence and sensitivity to learning parameters. Moreover, there is no unified neural network to compute the Moore–Penrose inverse for both the full‐rank matrix and rank‐deficient matrix. In this paper, an efficient second‐order neural network model with the improved Newton's method is proposed to obtain the accurate Moore–Penrose inverse of an arbitrary matrix by one epoch without any learning parameter. Compared with the GD‐based neural networks for Moore–Penrose inverse computation, the proposed model converges faster and has lower complexity. Furthermore, through in‐depth derivation, the neural network for computing the Moore–Penrose inverse is well interpretable. Numerical studies and application to the random matrix inversion in multiple‐input multiple‐output detection are provided to validate the efficiency of the proposed model for solving the Moore–Penrose inverse.https://doi.org/10.1049/sil2.12156arbitrary matriximproved Newton’s methodMoore‐Penrose inverseneural networksecond‐order model
spellingShingle Lin Li
Jianhao Hu
An efficient second‐order neural network model for computing the Moore–Penrose inverse of matrices
IET Signal Processing
arbitrary matrix
improved Newton’s method
Moore‐Penrose inverse
neural network
second‐order model
title An efficient second‐order neural network model for computing the Moore–Penrose inverse of matrices
title_full An efficient second‐order neural network model for computing the Moore–Penrose inverse of matrices
title_fullStr An efficient second‐order neural network model for computing the Moore–Penrose inverse of matrices
title_full_unstemmed An efficient second‐order neural network model for computing the Moore–Penrose inverse of matrices
title_short An efficient second‐order neural network model for computing the Moore–Penrose inverse of matrices
title_sort efficient second order neural network model for computing the moore penrose inverse of matrices
topic arbitrary matrix
improved Newton’s method
Moore‐Penrose inverse
neural network
second‐order model
url https://doi.org/10.1049/sil2.12156
work_keys_str_mv AT linli anefficientsecondorderneuralnetworkmodelforcomputingthemoorepenroseinverseofmatrices
AT jianhaohu anefficientsecondorderneuralnetworkmodelforcomputingthemoorepenroseinverseofmatrices
AT linli efficientsecondorderneuralnetworkmodelforcomputingthemoorepenroseinverseofmatrices
AT jianhaohu efficientsecondorderneuralnetworkmodelforcomputingthemoorepenroseinverseofmatrices