IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v73y2019i1d10.1007_s10898-018-0692-4.html
   My bibliography  Save this article

The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint

Author

Listed:
  • Baohua Huang

    (Fujian Normal University)

  • Changfeng Ma

    (Fujian Normal University)

Abstract

In this paper, we present an iterative method for finding the least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint. We prove that if the constrained matrix equations are consistent, the solution can be obtained within finite iterative steps in the absence of round-off errors; if constrained matrix equations are inconsistent, the least squares solution can be obtained within finite iterative steps in the absence of round-off errors. Finally, numerical examples are provided to illustrate the efficiency of the proposed method and testify the conclusions suggested in this paper.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jglopt:v:73:y:2019:i:1:d:10.1007_s10898-018-0692-4
    DOI: 10.1007/s10898-018-0692-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-018-0692-4
    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/s10898-018-0692-4?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. Magnus, J.R., 1983. "L-structured matrices and linear matrix equations," Other publications TiSEM ef9a74f0-816a-4079-8211-1, Tilburg University, School of Economics and Management.
    2. 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.
    3. Aijing Liu & Guoliang Chen & Xiangyun Zhang, 2013. "A New Method for the Bisymmetric Minimum Norm Solution of the Consistent Matrix Equations ," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, March.
    4. 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.
    5. Jiao-fen Li & Wen Li & Ru Huang, 2016. "An efficient method for solving a matrix least squares problem over a matrix inequality constraint," Computational Optimization and Applications, Springer, vol. 63(2), pages 393-423, March.
    6. Xie, Ya-Jun & Ma, Chang-Feng, 2016. "The accelerated gradient based iterative algorithm for solving a class of generalized Sylvester-transpose matrix equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1257-1269.
    7. 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.
    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. 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. 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.
    3. Zachary F. Fisher & Kenneth A. Bollen, 2020. "An Instrumental Variable Estimator for Mixed Indicators: Analytic Derivatives and Alternative Parameterizations," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 660-683, September.
    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. Zhang, Fengxia & Wei, Musheng & Li, Ying & Zhao, Jianli, 2015. "Special least squares solutions of the quaternion matrix equation AX=B with applications," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 425-433.
    6. 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).
    7. 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).
    8. 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).
    9. 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:spr:jglopt:v:73:y:2019:i:1:d:10.1007_s10898-018-0692-4. 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.