Application of Artificial Neural Network Method for Solving Nonlinear Equations

Abstract

In this thesis, we focused on the applications of Artificial neural network method and Aberth Ehrlich iterative method for solving nonlinear polynomial equations of arbitrary degree n. We studied Artificial neural network method for solving polynomials. We started by training the Artificial neural networks using the Long short term memory algorithm and as input the coefficients of the polynomials considered. We used feedback neural network and supervised learning method to update the network parameters. Two activation functions (Sigmoid activation function and hyperbolic tangent activation function) were used in this work. We used mean square error as loss function in order to update the weight and results were then compared in terms of accuracy and efficiency with the Aberth Ehrlich method. The comparisons are mainly based on their mean square error values and running time. The basic python code is used for implementation of the results in tables and graphs.