IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v369y2020ics0096300319308847.html
   My bibliography  Save this article

Global least squares methods based on tensor form to solve a class of generalized Sylvester tensor equations

Author

Listed:
  • Huang, Baohua
  • Ma, Changfeng

Abstract

This paper is concerned with some of well-known iterative methods in their tensor forms to solve a class of tensor equations via the Einstein product and the associated with least squares problem. Especially, the tensor forms of the LSQR and LSMR methods are presented. The proposed methods use tensor computations with no matricizations involved. We prove that the norm of residual is monotonically decreasing for the tensor form of the LSQR method. The norm of residual of normal equation is also monotonically decreasing for the tensor form of the LSMR method. We also show that the minimum-norm solution (or the minimum-norm least squares solution) of the tensor equation can be obtained by the proposed methods. Numerical examples are provided to illustrate the efficiency of the proposed methods and testify the conclusions suggested in this paper.

Suggested Citation

  • Huang, Baohua & Ma, Changfeng, 2020. "Global least squares methods based on tensor form to solve a class of generalized Sylvester tensor equations," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308847
    DOI: 10.1016/j.amc.2019.124892
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319308847
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.124892?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Xin-Fang & Wang, Qing-Wen, 2021. "Developing iterative algorithms to solve Sylvester tensor equations," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    2. Khosravi Dehdezi, Eisa & Karimi, Saeed, 2022. "A rapid and powerful iterative method for computing inverses of sparse tensors with applications," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    3. Eisa Khosravi Dehdezi, 2021. "Iterative Methods for Solving Sylvester Transpose Tensor Equation $$~\mathcal A\star _N\mathcal X\star _M\mathcal {B}+\mathcal {C}\star _M\mathcal X^T\star _N\mathcal {D}=\mathcal {E}$$ A ⋆ N X ⋆ M B ," SN Operations Research Forum, Springer, vol. 2(4), pages 1-21, December.
    4. Qi, Zhaohui & Ning, Yingqiang & Xiao, Lin & Luo, Jiajie & Li, Xiaopeng, 2023. "Finite-time zeroing neural networks with novel activation function and variable parameter for solving time-varying Lyapunov tensor equation," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    5. Xiao, Lin & Li, Xiaopeng & Jia, Lei & Liu, Sai, 2022. "Improved finite-time solutions to time-varying Sylvester tensor equation via zeroing neural networks," Applied Mathematics and Computation, Elsevier, vol. 416(C).

    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:eee:apmaco:v:369:y:2020:i:c:s0096300319308847. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.