Strict Interpolation of a Smooth Function and Its First Derivative Using a Linearly-Trained Radial Basis Function Neural Network

Abstract

We present a neural network, based on Gaussian functions, for interpolating a univariate function and its first derivative. The network is linearly trained, and constitutes a continuous piecewise approximation. It is based on the superposition of three standard Gaussian-based radial basis function networks. Analysis indicates that the network is a better approximation than the standard network.