Error Analysis of Parameter Prediction via Gaussian Process Regression and Its Application to Weighted Jacobi Iteration

Abstract

In this paper, we introduce a novel theoretical framework for Gaussian process regression error analysis, leveraging a function-space decomposition. Based on this framework, we develop a weighted Jacobi iterative method that utilizes Gaussian process regression for parameter prediction and provide a corresponding convergence analysis. Moreover, the convergence conditions are designed to be compatible with other error bounds, enabling a more general analysis. Experimental results show that the parameters predicted based on Gaussian process regression significantly accelerate the convergence speed of Jacobi iterations.