On the Continuity of Multivariate Lagrange Interpolation at Chung-Yao Lattices

TL;DR

This paper establishes a geometric condition under which Chung-Yao lattice-based multivariate Lagrange interpolation polynomials converge to the Taylor polynomial of sufficiently differentiable functions.

Contribution

It introduces a natural geometric criterion that guarantees convergence of Chung-Yao interpolation polynomials to Taylor polynomials.

Findings

Identifies a geometric condition for convergence.

Proves convergence of interpolation polynomials to Taylor polynomials.

Applicable to sufficiently differentiable functions.

Abstract

We give a natural geometric condition that ensures that sequences of Chung-Yao interpolation polynomials (of fixed degree) of sufficiently differentiable functions converge to a Taylor polynomial.