Computer Numerical Experiment Results of Zhang Neural Net Connected to Jacobi Iteration Algorithm for Static Linear Equation System Solving

Abstract

It is very common and vital to solve linear equation system (LES) in numerical fields. Generally, LES problems mainly include two types, i.e., the time-dependent LES problem and the static (i.e., time-independent) LES problem. With the rapid development of artificial intelligence, neural network has rich application scenes in many fields. For example, Zhang neural net (ZNN) is an effective neural network when solving time-dependent problems. In this paper, we present a special ZNN model termed elegant-formula ZNN (EFZNN) model. In addition, the specific EFZNN model has close relation with the traditional algorithm, i.e., Jacobi iteration (JI) algorithm, after ingenious construction and discretization by Euler forward discretization formula. Especially, when we fix the step-size in the discretization EFZNN algorithm as 1, it is the same as the JI algorithm. Besides, the ZNN and EFZNN models including the corresponding discretization algorithms for solving the LES are introduced, and the feasibility and efficiency of them in solving the LES are verified by, more importantly, computer numerical experiments, being the main merit of the paper.