Constructive Uniform Approximation of Differentiable Vector-Functions by Neural Network Methods

A method for constructively approximating any twice differentiable function in the uniform (i.e. maximal error) norm by successive changes in the weights and number of neurons in a neural network is developed. This is a realization of the approximation results of Cybenko, White, Gallant, Loshno and others. The constructive approximation in the uniform norm is more appropriate for, e.g. certain robotic applications, and stands in contrast with more standard methods, such as back-propagation which approximate only in the average error norm.