The Neural-Network Approaches to Solve Nonlinear Equation

Abstract

In this paper, we proposed two neural-network approaches for solving nonlinear equations or polynomials. The first method is suitable for finding simple roots of nonlinear equation or polynomial, and the second approach is fit to finding both the multiple and simple roots  of  nonlinear equations or polynomial, which were not well solved by the other methods. The convergence of algorithm proposed was researched. The convergence theorem provides the theory criterion selecting learning rate of neural network. The specific examples showed that the proposed method can find the simple or multiple roots of nonlinear equations or polynomials at a very rapid convergence and very high accuracy with less computation.