Matrix splitting iterative methods with parameters play a crucial role in solving linear systems. How to choose optimal splitting parameters is a key problem. In this talk, we propose a data-driven approach for predicting optimal iterative parameters: multi-task kernel learning Gaussian regression prediction (GPR) method. We develop the generalized alternating direction implicit (GADI) framework with optimal parameters, successfully integrating it as a smoother in algebraic multigrid methods to solve linear systems. Moreover, we accelerate GPR using mixed precision strategy and evaluate the predicted results with statistical indicators. Further, we have successfully applied GPR to (time-dependent) linear algebraic systems (elliptic equations, Poisson equations, convection-diffusion equations, Helmholtz equations) and linear matrix equations (Sylvester equations). Numerical results illustrate our methods can save an enormous amount of time in selecting the relatively optimal splitting parameters compared with the exists methods. When the system size exceeds hundreds of thousands, the acceleration ratio of the GADI framework can reach hundreds to thousands of times.
