From Standard ZND (Zhang Neural Dynamics) Solving Time-Variant Linear System (LS) to Elegant-Formula ZND Solving Time-Invariant LS Linked to Jacobi Iteration

Abstract

Solving linear system (LS) is a common and important issue in both academic and industrial fields. There are many methods to solve LS, including neural network (specifically, neural dynamics) and traditional numerical computation algorithms. Besides, traditional numerical computation algorithms comprise, but not limited to, Jacobi iteration and Gauss-Seidel iteration algorithms. On the other hand, neural network algorithms have been the hot topics in research for a long time, which are applied in various fields. In addition, standard Zhang neural dynamics (ZND) is a special kind of neural network to solve some time-variant problems effectively. In this paper, an elegant-formula ZND (EFZND) algorithm is obtained through theoretical derivation. Then, the standard ZND and different EFZND models for solving LS are introduced. Furthermore, the possible relationship between neural dynamics and traditional numerical computation algorithms, especially Jacobi iteration algorithm, is discussed from two specific EFZND models for solving LS. Finally, the feasibility and efficiency of standard ZND and EFZND models for solving LS are proved through derivation.