APPROXIMATING POLYNOMIAL FUNCTIONS BY FEEDFORWARD ARTIFICIAL NEURAL NETWORKS - CAPACITY ANALYSIS AND DESIGN

Polynomial functions are used in many applications. In this paper, we address the capacity of Feedforward Artificial Neural Networks (FANNs) in approximating polynomial functions. Instead of studying the capaci ty of a FANN with infinitely available hidden nodes, which was proved to be a universal approximator, we provide the capacity results of a F ANN with finite hidden nodes in approximating polynomial functions. Fi rst, we show that there is a relationship between the capacity of a FA NN in approximating polynomial functions and the number of hidden node s used in the FANN. Then, we describe a procedure to realize a FANN in approximating polynomial functions. Two examples are given to show th e procedure. Several experiments are reported which verifies that a FA NN with a certain number of hidden nodes has the capability in learnin g given polynomial functions. An extension of the approach for solving multiple criteria decision making problems is discussed. The experime nts also show that the proposed algorithm for training a FANN performs accurately. (C) Elsevier Science Inc., 1998.