Quadratic and related exponential splines in shape preserving interpolation

摘要

For quadratic and related exponential splines necessary and sufficient conditions are given under which the properties of convexity or monotonicity carry over from the data set to the interpolants. It turns out that for quadratic splines the problems of convex or monotone interpolation may be not solvable. However, when using the more general exponential splines, the shape is preserved if the parameters occuring now are chosen appropriately. Furthermore, since convex or monotone spline interpolants are in general not uniquely determined, a strategy for selecting one of them is proposed.