De Boor–Fix functionals and Hermite boundary conditions in the polynomial spline interpolation problem

By means of de Boor–Fix functionals Hermite boundary conditions in the problem of spline interpolation are obtained. It is shown that some of the first and last B-spline coefficients can be found by explicit formulas in terms of elementary symmetric functions and the remaining coefficients can be computed as a solution of a banded system of linear equations.