Fine-tuned cubic generalized composite spline interpolation with optimal parameter

Abstract

We develop a univariate C^2 generalized composite spline approximation method with an optimal parameter using Unified and Extended B-splines (UE-splines). These basis functions depend on a parameter that can be adjusted to minimize the error between data points and the approximation function. To determine the optimal parameter efficiently, we have introduced a fitting method based on genetic algorithms. This approach exploits the power of this algorithm. A numerical example is presented to analyze the effectiveness of our approach. We first examine the impact of the optimal parameter on the error bound and computational cost, and then compare our approximation model with existing interpolation methods.