Observations and guidelines on interpolation with radial basis function network for one dimensional approximation problem

This paper reports observations on the form and behavior of the coefficient matrix involved in the training of radial basis function (RBF) network for one dimensional learning (interpolation) problem. Based on these, the paper first introduces a faster way for training this particular RBF. Then it proposes a guideline on choosing the RBF spread value to ensure not only a good approximation quality, but also the least sensitivity to perturbations in training data and numerical inaccuracies during evaluation. With these results, a single dimensional approximation with RBF network becomes straightforward. Several function approximation examples are included to show the results of this proposed spread value.