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

Author

Listed:
  • 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
    Department of Visual Communications, Huzhou University, Huzhou 313000, China)

  • 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
    Data Recovery Key Laboratory of Sichun Province, Neijing Normal University, Neijiang 641100, China
    Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece)

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.

Suggested Citation

  • Wendong Jiang & Chia-Liang Lin & Vasilios N. Katsikis & Spyridon D. Mourtas & Predrag S. Stanimirović & Theodore E. Simos, 2022. "Zeroing Neural Network Approaches Based on Direct and Indirect Methods for Solving the Yang–Baxter-like Matrix Equation," Mathematics, MDPI, vol. 10(11), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1950-:d:832637
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    Citations

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    Cited by:

    1. Vladislav N. Kovalnogov & Ruslan V. Fedorov & Dmitry A. Generalov & Andrey V. Chukalin & Vasilios N. Katsikis & Spyridon D. Mourtas & Theodore E. Simos, 2022. "Portfolio Insurance through Error-Correction Neural Networks," Mathematics, MDPI, vol. 10(18), pages 1-14, September.
    2. Stanimirović, Predrag S. & Mourtas, Spyridon D. & Mosić, Dijana & Katsikis, Vasilios N. & Cao, Xinwei & Li, Shuai, 2024. "Zeroing neural network approaches for computing time-varying minimal rank outer inverse," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    3. Spyridon D. Mourtas & Chrysostomos Kasimis, 2022. "Exploiting Mean-Variance Portfolio Optimization Problems through Zeroing Neural Networks," Mathematics, MDPI, vol. 10(17), pages 1-20, August.
    4. Bolin Liao & Cheng Hua & Xinwei Cao & Vasilios N. Katsikis & Shuai Li, 2022. "Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation," Mathematics, MDPI, vol. 10(15), pages 1-17, August.
    5. Rabeh Abbassi & Houssem Jerbi & Mourad Kchaou & Theodore E. Simos & Spyridon D. Mourtas & Vasilios N. Katsikis, 2023. "Towards Higher-Order Zeroing Neural Networks for Calculating Quaternion Matrix Inverse with Application to Robotic Motion Tracking," Mathematics, MDPI, vol. 11(12), pages 1-21, June.

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