A piecewise cubic approximation and the smoothing of curves in an adaptation mode

A simple iterative method is proposed for the local approximation and the smoothing of functions using a three-point cubic spline. The method is based on the four-point transforms and the recursive least square method. A recurrent third order smoothing digital filter is derived. The speed of convergence is not worse than 1/n3. The algorithm uses small resources of memory and can be applied to digital signal processing, contour and track finding as well as for a numerical solution of practical problems. The efficiency and the noise stability of the algorithm are confirmed by examples. (author)