Zeroing Neural Network Approaches Based on Direct and Indirect Methods for Solving the Yang–Baxter-like Matrix Equation

Wendong Jiang, Chia-Liang Lin, Vasilios N. Katsikis, Spyridon D. Mourtas, Predrag S. Stanimirović and Theodore E. Simos
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Wendong Jiang: Department of Digital Media Art, School of Art and Design, Fuzhou University of International Studies and Trade, Fuzhou 350200, China
Chia-Liang Lin: General Department, National & Kapodistrian University of Athens, GR-34400 Euripus Campus, 15772 Athens, Greece
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
Predrag S. Stanimirović: Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
Theodore E. Simos: Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Mathematics, 2022, vol. 10, issue 11, 1-13

Abstract: This research introduces three novel zeroing neural network (ZNN) models for addressing the time-varying Yang–Baxter-like matrix equation (TV-YBLME) with arbitrary (regular or singular) real time-varying (TV) input matrices in continuous time. One ZNN dynamic utilizes error matrices directly arising from the equation involved in the TV-YBLME. Moreover, two ZNN models are proposed using basic properties of the YBLME, such as the splitting of the YBLME and sufficient conditions for a matrix to solve the YBLME. The Tikhonov regularization principle enables addressing the TV-YBLME with an arbitrary input real TV matrix. Numerical experiments, including nonsingular and singular TV input matrices, show that the suggested models deal effectively with the TV-YBLME.

Keywords: Yang–Baxter-like matrix equation (YBLME); zeroing neural network (ZNN); dynamical system; Tikhonov regularization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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