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Complex, Temporally Variant SVD via Real ZN Method and 11-Point ZeaD Formula from Theoretics to Experiments

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  • Jianrong Chen

    (School of Humanities and Management, Youjiang Medical University for Nationalities, Baise 533000, China
    School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China)

  • Xiangui Kang

    (School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China
    Key Laboratory of Machine Intelligence and Advanced Computing, Ministry of Education, Guangzhou 510006, China)

  • Yunong Zhang

    (School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518107, China)

Abstract

The complex, temporally variant singular value decomposition (SVD) problem is proposed and investigated in this paper. Firstly, the original problem is transformed into an equation system. Then, by using the real zeroing neurodynamics (ZN) method, matrix vectorization, Kronecker product, vectorized transpose matrix, and dimensionality reduction technique, a dynamical model, termed the continuous-time SVD (CTSVD) model, is derived and investigated. Furthermore, a new 11-point Zhang et al. discretization (ZeaD) formula with fifth-order precision is proposed and studied. In addition, with the use of the 11-point and other ZeaD formulas, five discrete-time SVD (DTSVD) algorithms are further acquired. Meanwhile, theoretical analyses and numerical experimental results substantiate the correctness and convergence of the proposed CTSVD model and DTSVD algorithms.

Suggested Citation

  • Jianrong Chen & Xiangui Kang & Yunong Zhang, 2025. "Complex, Temporally Variant SVD via Real ZN Method and 11-Point ZeaD Formula from Theoretics to Experiments," Mathematics, MDPI, vol. 13(11), pages 1-22, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1841-:d:1669402
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    References listed on IDEAS

    as
    1. Meichun Huang & Yunong Zhang, 2024. "Zhang Neuro-PID Control for Generalized Bi-Variable Function Projective Synchronization of Nonautonomous Nonlinear Systems with Various Perturbations," Mathematics, MDPI, vol. 12(17), pages 1-25, August.
    2. Zizhao Xie & Jingru Sun & Yiping Tang & Xin Tang & Oluyomi Simpson & Yichuang Sun, 2023. "A K-SVD Based Compressive Sensing Method for Visual Chaotic Image Encryption," Mathematics, MDPI, vol. 11(7), pages 1-20, March.
    3. Jianrong Chen & Xiangui Kang & Yunong Zhang, 2023. "Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices," Mathematics, MDPI, vol. 11(15), pages 1-18, July.
    4. Andrey Tsyganov & Yulia Tsyganova, 2024. "SVD-Based Parameter Identification of Discrete-Time Stochastic Systems with Unknown Exogenous Inputs," Mathematics, MDPI, vol. 12(7), pages 1-13, March.
    5. Conghuan Ye & Shenglong Tan & Jun Wang & Li Shi & Qiankun Zuo & Bing Xiong, 2025. "Double Security Level Protection Based on Chaotic Maps and SVD for Medical Images," Mathematics, MDPI, vol. 13(2), pages 1-24, January.
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