Constructive Trigonometric Function Approximation of Neural Networks

In this paper, we consider approximation to trigonometric polynomial function by using a one-hidden-layer feedforward neural networks, and obtain the upper bounds of trigonometric function approximation by feedforward neural networks. Then we give the algorithmic example, where the networks constructed can very efficiently approximate multivariate trigonometric polynomials. The obtained results are of theoretical and practical importance in constructing a feedforward neural network with three-layer to approximate the class of multivariate trigonometric polynomials. They also provide a route in both theory and method of constructing neural network to approximate any multi- functions.