IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v328y2018icp58-74.html
   My bibliography  Save this article

An iterative algorithm for the least Frobenius norm least squares solution of a class of generalized coupled Sylvester-transpose linear matrix equations

Author

Listed:
  • Huang, Baohua
  • Ma, Changfeng

Abstract

The iterative algorithm of a class of generalized coupled Sylvester-transpose matrix equations is presented. We prove that if the system is consistent, a solution can be obtained within finite iterative steps in the absence of round-off errors for any initial matrices; if the system is inconsistent, the least squares solution can be obtained within finite iterative steps in the absence of round-off errors. Furthermore, we provide a method for choosing the initial matrices to obtain the least Frobenius norm least squares solution of the problem. Finally, numerical examples are presented to demonstrate that the algorithm is efficient.

Suggested Citation

  • Huang, Baohua & Ma, Changfeng, 2018. "An iterative algorithm for the least Frobenius norm least squares solution of a class of generalized coupled Sylvester-transpose linear matrix equations," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 58-74.
    • Handle: RePEc:eee:apmaco:v:328:y:2018:i:c:p:58-74
    DOI: 10.1016/j.amc.2018.01.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031830033X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.01.020?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. Mehdi Dehghan & Masoud Hajarian, 2012. "The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(8), pages 1580-1590.
    2. Masoud Hajarian, 2016. "Least Squares Solution of the Linear Operator Equation," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 205-219, July.
    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. Yan, Tongxin & Ma, Changfeng, 2021. "An iterative algorithm for generalized Hamiltonian solution of a class of generalized coupled Sylvester-conjugate matrix equations," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    2. Fu, Chunhong & Chen, Jiajia & Xu, Qingxiang, 2021. "Upper bounds and lower bounds for the Frobenius norm of the solution to certain structured Sylvester equation," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    3. Baohua Huang & Changfeng Ma, 2019. "The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint," Journal of Global Optimization, Springer, vol. 73(1), pages 193-221, January.

    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. Hu, Jingjing & Ma, Changfeng, 2018. "Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester-conjugate matrix equations," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 174-191.
    2. Baohua Huang & Changfeng Ma, 2019. "The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint," Journal of Global Optimization, Springer, vol. 73(1), pages 193-221, January.
    3. Qu, Hongli & Xie, Dongxiu & Xu, Jie, 2021. "A numerical method on the mixed solution of matrix equation ∑i=1tAiXiBi=E with sub-matrix constraints and its application," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    4. Xie, Ya-Jun & Ma, Chang-Feng, 2015. "The MGPBiCG method for solving the generalized coupled Sylvester-conjugate matrix equations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 68-78.
    5. repec:taf:tsysxx:v:46:y:2015:i:3:p:488-502 is not listed on IDEAS

    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:328:y:2018:i:c:p:58-74. 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.