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

Author

Listed:
  • 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
    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

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.

Suggested Citation

  • Mariya Kornilova & Vladislav Kovalnogov & Ruslan Fedorov & Mansur Zamaleev & Vasilios N. Katsikis & Spyridon D. Mourtas & Theodore E. Simos, 2022. "Zeroing Neural Network for Pseudoinversion of an Arbitrary Time-Varying Matrix Based on Singular Value Decomposition," Mathematics, MDPI, vol. 10(8), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1208-:d:788822
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    References listed on IDEAS

    as
    1. Francisco J. Valverde-Albacete & Carmen Peláez-Moreno, 2020. "The Singular Value Decomposition over Completed Idempotent Semifields," Mathematics, MDPI, vol. 8(9), pages 1-39, September.
    2. Daniel K. Crane & Mark S. Gockenbach, 2020. "The Singular Value Expansion for Arbitrary Bounded Linear Operators," Mathematics, MDPI, vol. 8(8), pages 1-12, August.
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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. Houssem Jerbi & Hadeel Alharbi & Mohamed Omri & Lotfi Ladhar & Theodore E. Simos & Spyridon D. Mourtas & Vasilios N. Katsikis, 2022. "Towards Higher-Order Zeroing Neural Network Dynamics for Solving Time-Varying Algebraic Riccati Equations," Mathematics, MDPI, vol. 10(23), pages 1-16, November.
    3. Xingyuan Li & Chia-Liang Lin & Theodore E. Simos & Spyridon D. Mourtas & Vasilios N. Katsikis, 2022. "Computation of Time-Varying {2,3}- and {2,4}-Inverses through Zeroing Neural Networks," Mathematics, MDPI, vol. 10(24), pages 1-13, December.
    4. 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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