Which Cubic Spline should One Use?

The aim of this paper is to provide a quantitative comparison of eight different 0 1 and 0 2 cubic spline interpolation schemes. The 0 1 schemes discussed are local while the 0 2 ones are global. In practice cubic splines are often used when the smoothness of the function being interpolated/approximated is unknown. Also it is often necessary, or advantageous, to use a nonuniform mesh. Therefore we compare performance over a variety of smoothness classes, using uniform and also several thousand random meshes. The performance criteria used are the quantitative ones of exact operator and derived operator norms, and best possible pointwise error estimates.