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

Kai Jiang, Jianghao Su and Juan Zhang ()
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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

Mathematics, 2022, vol. 10, issue 20, 1-24

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.

Keywords: Gaussian process regression; matrix-splitting iterative method; data-driven method; HSS iteration method; LHSS iteration method; NHSS iteration method; SHSS iteration method; SHSS-SS iteration method; MHSS iteration method; MSNS iteration method; linear systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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