High-degree splines from discrete Fourier transforms: Robust methods to obtain the boundary conditions

Computing accurate splines of degree greater than three is still a challenging task in today's applications. In this type interpolation, high-order derivatives are needed on the given mesh. As these rarely known and often not easy to approximate accurately, high-degree difficult obtain using standard approaches. Beaudoin (1998), Beauchemin (2003), Pepin et al. (2019), new method compute spline approximations low or high from equidistant interpolation nodes based discrete Fourier transform analyzed. The accuracy greatly depends boundary conditions. An algorithm for computation conditions can be found (2003). However, lacks robustness since approximation strongly dependant choice θ arbitrary parameters, being spline. goal paper therefore propose two robust algorithms, independent order any degree. Numerical results will presented show efficiency