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Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices

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  • Jianrong Chen

    (School of Public Health and Management, Youjiang Medical University for Nationalities, Baise 533000, China
    Guangdong Key Lab of Information Security, 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)

  • Xiangui Kang

    (Guangdong Key Lab of Information Security, 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

    (Guangdong Key Lab of Information Security, 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)

Abstract

The problem of QR decomposition is considered one of the fundamental problems commonly encountered in both scientific research and engineering applications. In this paper, the QR decomposition for complex-valued time-varying matrices is analyzed and investigated. Specifically, by applying the zeroing neural dynamics (ZND) method, dimensional reduction method, equivalent transformations, Kronecker product, and vectorization techniques, a new continuous-time QR decomposition (CTQRD) model is derived and presented. Then, a novel eleven-instant Zhang et al discretization (ZeaD) formula, with fifth-order precision, is proposed and studied. Additionally, five discrete-time QR decomposition (DTQRD) models are further obtained by using the eleven-instant and other ZeaD formulas. Theoretical analysis and numerical experimental results confirmed the correctness and effectiveness of the proposed continuous and discrete ZND models.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3354-:d:1207483
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    References listed on IDEAS

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    1. Daniel Ríos-Rivera & Jorge D. Rios & Oscar D. Sanchez & Alma Y. Alanis, 2022. "Impulsive Pinning Control of Discrete-Time Complex Networks with Time-Varying Connections," Mathematics, MDPI, vol. 10(21), pages 1-14, November.
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    Cited by:

    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.

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