Static Linear Algebra Problems Solving via Elegant Design Formula and Simplified Explicit Form of Zhang Neural Network with Illustrative Instances

Owing to the parallelism feature and convenient hardware implementation of recurrent neural network (RNN), many RNN models have been proposed to solve linear and nonlinear algebra problems. There into, Zhang neural network (ZNN) and gradient neural network (GNN) have received considerable attention and been exploited to investigate various dynamic models for solving various issues. However, the ZNN and GNN are depicted in quite rigorous formulations, which may limit the development of methodology of dynamic model design. This paper considers developing a new RNN design method named simplified Zhang neural network (SZNN) with more general formulation and versatile instances for statics. The comparisons between SZNN and two conventional methods are analyzed through theoretical results and simulation experiments of linear equation. Furthermore, to show the effectiveness and versatility of SZNN, Sylvester equation and matrix inversion are solved by the proposed SZNN models, and the simulation results substantiate the excellent convergence of the SZNN models.