Zeroing Neural Network for Pseudoinversion of an Arbitrary Time-Varying Matrix Based on Singular Value Decomposition

Mariya Kornilova, Vladislav Kovalnogov, Ruslan Fedorov, Mansur Zamaleev, Vasilios N. Katsikis, Spyridon D. Mourtas and Theodore E. Simos
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Mariya Kornilova: Laboratory of Inter-Disciplinary Problems in Clean Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
Vladislav Kovalnogov: Laboratory of Inter-Disciplinary Problems in Clean Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
Ruslan Fedorov: Laboratory of Inter-Disciplinary Problems in Clean Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
Mansur Zamaleev: Laboratory of Inter-Disciplinary Problems in Clean Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
Vasilios N. Katsikis: Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece
Spyridon D. Mourtas: Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece
Theodore E. Simos: Laboratory of Inter-Disciplinary Problems in Clean Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia

Mathematics, 2022, vol. 10, issue 8, 1-12

Abstract: Many researchers have investigated the time-varying (TV) matrix pseudoinverse problem in recent years, for its importance in addressing TV problems in science and engineering. In this paper, the problem of calculating the inverse or pseudoinverse of an arbitrary TV real matrix is considered and addressed using the singular value decomposition (SVD) and the zeroing neural network (ZNN) approaches. Since SVD is frequently used to compute the inverse or pseudoinverse of a matrix, this research proposes a new ZNN model based on the SVD method as well as the technique of Tikhonov regularization, for solving the problem in continuous time. Numerical experiments, involving the pseudoinversion of square, rectangular, singular, and nonsingular input matrices, indicate that the proposed models are effective for solving the problem of the inversion or pseudoinversion of time varying matrices.

Keywords: singular value decomposition (SVD); zeroing neural network (ZNN); Moore–Penrose inverse; Tikhonov regularization; dynamical system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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