A Note on Obtaining Natural Spline Functions by the Abstract Approach of Laurent

摘要

The natural spline functions interpolating data on (a, b) are obtained constructively by the abstract variational approach of Laurent. The (as yet unpublished) theorem of Laurent is stated and applied in the present context to yield an algorithm for the calculation of the splines. The emphasis of the paper is to set the splines in the Hilbert space framework via the theorem of Laurent. (Author)