Estimation of Calculation Time of Iterative Linear Equation Solvers Using Deep Learning － Proposal of Learning Model and its Feasibility Evaluation －

Abstract

This study aims to propose a method for selecting parameters of a linear equation solver considering properties of coefficient matrix, analysis method, and computer environments. We propose a learning model that appropriately selects parameters of a linear equation solver, for example types of iterative solvers and preconditioners, by machine learning based on various examples. The proposed method builds a neural network for each combination of iterative linear solvers and preconditonors, and estimates the required number of iterations using the features of coefficient matrix. Estimating the number of iterations, we can obtain the computation time by a simple benchmark for each computer, which can be used as an indicator to select parameters of the linear solver. In order to evaluate the feasibility of the proposed method, an automatic matrixgeneration system was also established. As a numerical example, the generalization performance was evaluated by the cross-validation method.