IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v170y2016i1d10.1007_s10957-015-0737-5.html
   My bibliography  Save this article

Least Squares Solution of the Linear Operator Equation

Author

Listed:
  • Masoud Hajarian

    (Shahid Beheshti University)

Abstract

The least squares problems have wide applications in inverse Sturm–Liouville problem, particle physics and geology, inverse problems of vibration theory, control theory, digital image and signal processing. In this paper, we discuss the solution of the operator least squares problem. By extending the conjugate gradient least squares method, we propose an efficient matrix algorithm for solving the operator least squares problem. The matrix algorithm can find the solution of the problem within a finite number of iterations in the absence of round-off errors. Some numerical examples are given to illustrate the effectiveness of the matrix algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:1:d:10.1007_s10957-015-0737-5
    DOI: 10.1007/s10957-015-0737-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-015-0737-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-015-0737-5?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. repec:taf:tsysxx:v:46:y:2015:i:3:p:488-502 is not listed on IDEAS
    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. 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).
    2. 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.
    3. 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.
    4. 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.

    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:spr:joptap:v:170:y:2016:i:1:d:10.1007_s10957-015-0737-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.