Rational cubic Ball curves for monotone data

Abstract

Abstract.A problem of monotonicity preserving interpolation is discussed in this presentation. If a given set of data is monotonic, we want the interpolant to also be monotonic. A rational interpolation scheme is developed. This scheme utilizes piecewise rational cubic Ball functions with four shape parameters in its description. Sufficient conditions to preserve the shape inherent in the data are derived. Three parameters will be allowed for a designer to further refine or control the shape of the curve, if desired. The arithmetic mean algorithm is used to approximate the first derivative at each data point. The degree of smoothness is C 1 . A number of numerical examples are presented.