MONOTONE PIECEWISE CURVE-FITTING ALGORITHMS

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[8] and Gasparo-Morandi's algorithm[5] for accurate or 0(h(q)) accUrate given data, but it has a more visually pleasing curve than those two algorithms. We also discuss the convergence order of cubic rational interpolation for 0(h(q)) accurate data.