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

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.