Defining and computing cubic splines

Abstract

In this note we address the students’ usual misperception of the cubic spline definition and construction within an undergraduate numerical course in order to present an alternative initial approach. We describe succinctly the standard path from the interpolating polynomial towards a smooth piecewise interpolation model and we focus on a simpler, though unstable, cubic spline structure. This less common choice aims to promote a more comprehensible dialogue between the notion of cubic spline functions and the numerical (in)adequacy of different methods for computing such functions.