Rational splines for Hermite interpolation with shape constraints Original Research Article

This paper is concerned in shape-preserving Hermite interpolation of a given function f at the endpoints of an interval using rational functions. After a brief presentation of the general Hermite problem, we investigate two cases. In the first one, f and image are given and it is proved that for any monotonic set of data, it is always possible to construct a monotonic rational function of type image interpolating those data. Positive and convex interpolants can be computed by a similar method. In the second case, results are proved using rational function of type image for interpolating the data coming from f, image and image with the goal of constructing positive, monotonic or convex interpolants. Error estimates are given and numerical examples illustrate the algorithms.