Polynomial Fitting Algorithm Based on Neural Network

Abstract

As a method of function approximation, polynomial fitting has always been the main research hotspot in mathematical modeling. In many disciplines such as computer, physics, biology, neural networks have been widely used, and most of the applications have been transformed into fitting problems using neural networks. One of the main reasons that neural networks can be widely used is that it has a certain sense of universal approximation. In order to fit the polynomial, this paper constructs a three-layer feedforward neural network, uses Taylor series as the activation function, and determines the number of hidden layer neurons according to the order of the polynomial and the dimensions of the input variables. For explicit polynomial fitting, this paper uses non-linear functions as the objective function, and compares the fitting effects under different orders of polynomials. For the fitting of implicit polynomial curves, the current popular polynomial fitting algorithms are compared and analyzed. Experiments have proved that the algorithm used in this paper is suitable for both explicit polynomial fitting and implicit polynomial fitting. The algorithm is relatively simple, practical, easy to calculate, and can efficiently achieve the fitting goal. At the same time, the computational complexity is relatively low, which has certain application value.