PIECEWISE CUBIC MONOTONE-INTERPOLATION WITH ASSIGNED SLOPES

An algorithm to construct a monotonicity preserving cubic C1 interpolant without modification of the assigned slopes is proposed. An O(h4) convergence result is obtained when exact function and derivative values are available and O(h(p)) convergence can be obtained with p = min(4, q) for O(h(q)) accurate function and derivative values. Numerical experiments carried out on data coming from functions with very different behaviours are presented. The results show that the method can interpolate monotone data in a visually pleasing way, even for data which present rapid variations.