Monotone Piecewise Curve Fitting Algorithms

Abstract

A piecewise cubic curve fitting algorithm preserving monotonicity of the data without modification of the assigned slopes is proposed. The algorithm has the same order of convergence as Yan's algorithm and Gasparo-Morandi's algorithm for accurate or $O(h^q)$ accurate give date, but it has a more visually pleasing curve that those two algorithms. We also discuss the convergence order of cubic rational interpolation for $O(h^q)$ accurate date.