Constructing Feedforward Neural Networks to Approximate Polynomial Functions
CAO FeiLong1,2, ZHANG YongQuan1, PAN Xing1
1.Department of Information and Mathematics Sciences, China Jiliang University, Hangzhou 310018 2.Institute for Information and System Sciences, Xi’an Jiaotong University, Xi’an 710049
Abstract It is investigated that multivariate polynomial functions with n order are approximated by feedforward neural networks with three layers. Firstly, for a given polynomial function with n order, a feedforward neural network with three layers is designed by a constructive method to approximate the polynomial with any degree of accuracy. The number of hidden layer nodes of the constructed network only depends on the order and dimension of approximated polynomial. Then, an algorithm to realize the approximation is given. Finally, two numerical examples are given for further illustration of the results. The obtained results have a guidance signification to construct feedforward neural networks with three layers to approximate the class of polynomial functions and realize the approximation.
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2007, Vol. 20 
