IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i20p3789-d942240.html
   My bibliography  Save this article

A Data-Driven Parameter Prediction Method for HSS-Type Methods

Author

Listed:
  • Kai Jiang

    (Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China)

  • Jianghao Su

    (School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China)

  • Juan Zhang

    (Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan 411105, China)

Abstract

Some matrix-splitting iterative methods for solving systems of linear equations contain parameters that need to be specified in advance, and the choice of these parameters directly affects the efficiency of the corresponding iterative methods. This paper uses a Bayesian inference-based Gaussian process regression (GPR) method to predict the relatively optimal parameters of some HSS-type iteration methods and provide extensive numerical experiments to compare the prediction performance of the GPR method with other existing methods. Numerical results show that using GPR to predict the parameters of the matrix-splitting iterative methods has the advantage of smaller computational effort, predicting more optimal parameters and universality compared to the currently available methods for finding the parameters of the HSS-type iteration methods.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3789-:d:942240
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/20/3789/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/20/3789/
    Download Restriction: no
    ---><---

    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. Hadjidimos, A. & Yeyios, A., 1982. "Symmetric accelerated overrelaxation (SAOR) method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 24(1), pages 72-76.
    3. 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.
    4. Chen, Fang, 2015. "On choices of iteration parameter in HSS method," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 832-837.
    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. 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).
    2. Huang, Zheng-Ge & Wang, Li-Gong & Xu, Zhong & Cui, Jing-Jing, 2017. "The generalized modified shift-splitting preconditioners for nonsymmetric saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 95-118.
    3. 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.
    4. Huang, Zheng-Ge & Wang, Li-Gong & Xu, Zhong & Cui, Jing-Jing, 2020. "An efficient preconditioned variant of the PSS preconditioner for generalized saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    5. 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).
    6. 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.
    7. Chein-Shan Liu & Essam R. El-Zahar & Chih-Wen Chang, 2023. "Dynamical Optimal Values of Parameters in the SSOR, AOR, and SAOR Testing Using Poisson Linear Equations," Mathematics, MDPI, vol. 11(18), pages 1-21, September.
    8. Ling, Si-Tao & Liu, Qing-Bing, 2017. "New local generalized shift-splitting preconditioners for saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 58-67.

    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:gam:jmathe:v:10:y:2022:i:20:p:3789-:d:942240. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.