Zhang-Taylor Type Newton Iterations (NI) Handling Nonlinear Equation, Nonlinear Equation System, and Matrix Inverse, in Addition to Euler-Type NI

Nonlinear equation, nonlinear equation system (NES), and matrix inverse are critical topics in contemporary research. In this paper, we utilize Zhang dynamics (ZD, or termed, Zhang neural dynamics, Zhang neural network) and Newton iterations (NI) for handling the nonlinear equation, NES, and matrix inverse. For more efficient computation and easier implementation in digital computer, we propose a novel Zhang-Taylor type (ZT-type) NI by using the ZT-type 1-step-ahead numerical differentiation rule to discretize the continuous ZD (CZD) model. Moreover, numerical experimental results show the feasibility and effectiveness of the ZT-type NI for handling nonlinear equation, NES, and matrix inverse. Besides, comparative experimental results show that the ZT-type NI is comparable with the Euler-type NI.