Discrete Interpolating and Smoothing Spline Functions

Abstract

This paper uses the results of Anselone and Laurent to carry out discrete interpolation and smoothing, which give rise to discrete natural polynomial spline functions. The discrete interpolation is a generalization of work done by Vaughan and Greville. The discrete smoothing generalizes work done by Whittaker. Both discrete spline interpolation and smoothing are shown to be smoothing processes in a sense defined by Greville. The algorithms developed for the discrete natural cubic spline case are shown to be good computational procedures.