Hilbertian Interpolation

TL;DR

This paper aims to demonstrate that various classical interpolation and approximation methods can be unified under a single Hilbertian framework, simplifying understanding and potentially improving techniques.

Contribution

It introduces a unified Hilbertian scheme that underpins all classical interpolation and approximation methods, providing a new perspective on their interrelations.

Findings

Classical interpolation methods can be derived from a single Hilbertian scheme.

The approach simplifies understanding of various interpolation techniques.

Potential for generalization to more complex examples.

Abstract

I want to prove that all classical techniques of interpolation and approximation as Lagrange, Taylor, Hermite interpolations Beziers interpolants, Quasi interpolants, Box splines and others (radial splines, simplicial splines) are derived from a \textbf{unique} simple hilbertian scheme. For sake of simplicity, we shall consider only elementary examples which could be easily generalized.