IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v422y2022ics0096300322000704.html
   My bibliography  Save this article

Preconditioned TBiCOR and TCORS algorithms for solving the Sylvester tensor equation

Author

Listed:
  • Huang, Guang-Xin
  • Chen, Qi-Xing
  • Yin, Feng

Abstract

In this paper, the preconditioned TBiCOR and TCORS methods are presented for solving the Sylvester tensor equation. A tensor Lanczos L-Biorthogonalization algorithm (TLB) is derived for solving the Sylvester tensor equation. Two improved TLB methods are presented. One is the biconjugate L-orthogonal residual algorithm in tensor form (TBiCOR), which implements the LU decomposition for the triangular coefficient matrix derived by the TLB method. The other is the conjugate L-orthogonal residual squared algorithm in tensor form (TCORS), which introduces a square operator to the residual of the TBiCOR algorithm. A preconditioner based on the nearest Kronecker product is used to accelerate the TBiCOR and TCORS algorithms, and we obtain the preconditioned TBiCOR algorithm (PTBiCOR) and preconditioned TCORS algorithm (PTCORS). The proposed algorithms are proved to be convergent within finite steps of iteration without roundoff errors. Several examples illustrate that the preconditioned TBiCOR and TCORS algorithms present excellent convergence.

Suggested Citation

  • Huang, Guang-Xin & Chen, Qi-Xing & Yin, Feng, 2022. "Preconditioned TBiCOR and TCORS algorithms for solving the Sylvester tensor equation," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    • Handle: RePEc:eee:apmaco:v:422:y:2022:i:c:s0096300322000704
    DOI: 10.1016/j.amc.2022.126984
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322000704
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.126984?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.

    References listed on IDEAS

    as
    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. Zhen Chen & Linzhang Lu, 2013. "A Gradient Based Iterative Solutions for Sylvester Tensor Equations," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, March.
    3. Lv, Changqing & Ma, Changfeng, 2020. "A modified CG algorithm for solving generalized coupled Sylvester tensor equations," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Chen, Qi-Xing & Huang, Guang-Xin & Zhang, Ming-Yue, 2024. "Preconditioned BiCGSTAB and BiCRSTAB methods for solving the Sylvester tensor equation," Applied Mathematics and Computation, Elsevier, vol. 466(C).

    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. Chen, Qi-Xing & Huang, Guang-Xin & Zhang, Ming-Yue, 2024. "Preconditioned BiCGSTAB and BiCRSTAB methods for solving the Sylvester tensor equation," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    2. 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).
    3. Tao Li & Qing-Wen Wang & Xin-Fang Zhang, 2022. "A Modified Conjugate Residual Method and Nearest Kronecker Product Preconditioner for the Generalized Coupled Sylvester Tensor Equations," Mathematics, MDPI, vol. 10(10), pages 1-19, May.
    4. Zhang, Xin-Fang & Wang, Qing-Wen, 2021. "Developing iterative algorithms to solve Sylvester tensor equations," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    5. 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).

    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:422:y:2022:i:c:s0096300322000704. 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: 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.