A new spline approach for data fitting

This paper presents an extension of the Modified Spline Technique (MST) formulation for data fitting named power spline, which gives consistent results for sets of data of concave and convex curves. This method is based on a technique which couples an implicit formulation of the maximum likelihood principle to the spline method, making the method suitable to fit data when no physical model is available. The MST method proved to be better than to the spline method and the extended spline fit technique (EST), because it provided accurate results for the first and second derivatives in sets of data where the EST solution developed inaccuracies. The EST method is a formulation that couples Least Squares to the spline method. There are, however, some sets of data where the MST method would show inconsistent solutions for the first and second derivatives. The power spline method eliminates these problems for concave or convex curves. Another improvement on the method is a more flexible choice for the interval boundaries.1A free version of this software is available at http://www.feq.unicamp.br/~nunhez.