Approximating functions by neural networks: A constructive solution in the uniform norm

A method for constructively approximating functions 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, Hecht-Nielsen, Hornik, Stinchcombe, White, Callant, Funahashi, Leshno et al., and others. The constructive approximation in the uniform norm is more appropriate for a number of examples, such as robotic arm motion, and stands in contrast with more standard methods, such as back-propagation, which approximate only in the average error norm.