Optimizing at the end-points the Akima's interpolation method of smooth curve fitting

In this paper we propose an optimized version, at the end-points, of the Akima's interpolation method for experimental data fitting. Comparing with the Akima's procedure, the error estimate, in terms of the modulus of continuity, is improved. Similarly, we optimize at the end points the Catmull–Rom's cubic spline. The properties of the obtained splines are illustrated on a numerical experiment.