Approximation of Polynomial Functions by Neural Network: Construction of Network and Algorithm of Approximation
Fei Cao · Chinese Journal of Computers · 2003
It is investigated in this paper that the polynomial functions are approximated by feed-forward neural network with three-layer. Firstly, It is shown that for a given polynomial function with r order a feed-forward neural network with three-layer can be constructed by a constructive method to approximate the polynomial to any degree of accuracy. The number of hidden-layer nodes of the constructed network only depends on the order of approximated polynomial and the number of input of the network. It can also be expressed by the order of approximated polynomial accurately. Then, an algorithm to realize the approximation is given. Finally, two numerical examples are given for further illustrating the results. The obtained results are more important for constructing a feed-forward neural network with three-layer to approximate the class of polynomial functions and for realizing the approximation.