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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
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    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.
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