IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i15p3354-d1207483.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/15/3354/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/15/3354/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    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. Hadeel Alharbi & Houssem Jerbi & Mourad Kchaou & Rabeh Abbassi & Theodore E. Simos & Spyridon D. Mourtas & Vasilios N. Katsikis, 2023. "Time-Varying Pseudoinversion Based on Full-Rank Decomposition and Zeroing Neural Networks," Mathematics, MDPI, vol. 11(3), pages 1-14, January.
    4. Sneha Jadhav & Jianxiang Zhao & Yepeng Fan & Jingjing Li & Hao Lin & Chenggang Yan & Minghan Chen, 2023. "Time-Varying Sequence Model," Mathematics, MDPI, vol. 11(2), pages 1-15, January.
    5. Xikui Liu & Wencong Li & Chenxin Yao & Yan Li, 2022. "Finite-Time Guaranteed Cost Control for Markovian Jump Systems with Time-Varying Delays," Mathematics, MDPI, vol. 10(12), pages 1-12, June.
    6. Andrei Tănăsescu & Mihai Carabaş & Florin Pop & Pantelimon George Popescu, 2021. "Scalability of k -Tridiagonal Matrix Singular Value Decomposition," Mathematics, MDPI, vol. 9(23), pages 1-11, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Houssem Jerbi & Obaid Alshammari & Sondess Ben Aoun & Mourad Kchaou & Theodore E. Simos & Spyridon D. Mourtas & Vasilios N. Katsikis, 2023. "Hermitian Solutions of the Quaternion Algebraic Riccati Equations through Zeroing Neural Networks with Application to Quadrotor Control," Mathematics, MDPI, vol. 12(1), pages 1-19, December.
    3. Khanh Hieu Nguyen & Sung Hyun Kim, 2022. "Event-Triggered Non-PDC Filter Design of Fuzzy Markovian Jump Systems under Mismatch Phenomena," Mathematics, MDPI, vol. 10(16), pages 1-25, August.
    4. Guoqiang Sun & Xiaoyan Qi & Qiang Zhao & Wei Wang & Yujun Li, 2024. "SVSeq2Seq: An Efficient Computational Method for State Vectors in Sequence-to-Sequence Architecture Forecasting," Mathematics, MDPI, vol. 12(2), pages 1-17, January.
    5. Xinlan Guo & Mohammadamin Shirkhani & Emad M. Ahmed, 2022. "Machine-Learning-Based Improved Smith Predictive Control for MIMO Processes," Mathematics, MDPI, vol. 10(19), pages 1-19, October.
    6. Aravindh Dharmarajan & Parivallal Arumugam & Sakthivel Ramalingam & Kavikumar Ramasamy, 2023. "Equivalent-Input-Disturbance Based Robust Control Design for Fuzzy Semi-Markovian Jump Systems via the Proportional-Integral Observer Approach," Mathematics, MDPI, vol. 11(11), pages 1-16, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3354-:d:1207483. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.