Shape Preserving C³ Data Interpolation and C³ Histopolation with Splines on Threefold Refined Grids

Abstract

This paper is concerned with the convex C3 interpolation of univariate data sets. An algorithm based on the use of quartic splines on threefold refined girds is presented which is always successful for data sets in strictly convex position. These splines are suitable also for monotone as well as positive C3 interpolation. Further, the derived algorithms apply to the monotone and positive C2 histopolation with cubic splines on grids refined as before.