IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v399y2021ics0096300321000552.html
   My bibliography  Save this article

Upper bounds and lower bounds for the Frobenius norm of the solution to certain structured Sylvester equation

Author

Listed:
  • Fu, Chunhong
  • Chen, Jiajia
  • Xu, Qingxiang

Abstract

This paper studies the Frobenius norm upper bounds and lower bounds of the unique solution to AX+XB=AC+DB, where A∈Cm×m and B∈Cn×n are Hermitian positive definite, and C,D∈Cm×n are arbitrary. Some theoretical improvements of the known results are made. Numerical tests to illustrate the sharpness of the newly obtained upper bounds are dealt with, and numerical examples associated with the positivity of lower bounds are also provided.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:399:y:2021:i:c:s0096300321000552
    DOI: 10.1016/j.amc.2021.126007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321000552
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126007?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. Dehghan, Mehdi & Shirilord, Akbar, 2019. "A generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equation," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 632-651.
    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. Liu, Na & Luo, Wei & Xu, Qingxiang, 2018. "New multiplicative perturbation bounds for the generalized polar decomposition," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 259-271.
    4. Zhou, Rong & Wang, Xiang & Tang, Xiao-Bin, 2015. "A generalization of the Hermitian and skew-Hermitian splitting iteration method for solving Sylvester equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 609-617.
    5. Hu, Li-Ying & Guo, Gong-De & Ma, Chang-Feng, 2015. "The least squares anti-bisymmetric solution and the optimal approximation solution for Sylvester equation," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 212-219.
    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. Kai Jiang & Jianghao Su & Juan Zhang, 2022. "A Data-Driven Parameter Prediction Method for HSS-Type Methods," Mathematics, MDPI, vol. 10(20), pages 1-24, October.
    2. Hai-Long Shen & Yan-Ran Li & Xin-Hui Shao, 2019. "The Four-Parameter PSS Method for Solving the Sylvester Equation," Mathematics, MDPI, vol. 7(1), pages 1-13, January.
    3. Fu, Chunhong & Xu, Qingxiang, 2020. "An optimal perturbation bound for the partial isometry associated to the generalized polar decomposition," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    4. Dehghan, Mehdi & Shirilord, Akbar, 2019. "A generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equation," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 632-651.
    5. 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).
    6. Devi, Vinita & Maurya, Rahul Kumar & Singh, Somveer & Singh, Vineet Kumar, 2020. "Lagrange’s operational approach for the approximate solution of two-dimensional hyperbolic telegraph equation subject to Dirichlet boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    7. 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:eee:apmaco:v:399:y:2021:i:c:s0096300321000552. 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.