Revista Matemática Iberoamericana

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Volume 27, Issue 1, 2011, pp. 355–360
DOI: 10.4171/RMI/639

Published online: 2011-04-30

The Jet of an Interpolant on a Finite Set

Charles Fefferman[1] and Arie Israel[2]

(1) Princeton University, United States
(2) University of Texas at Austin, USA

We study functions $F \in C^m (\mathbb{R}^n)$ having norm less than a given constant $M$, and agreeing with a given function $f$ on a finite set $E$. Let $\Gamma_f (S,M)$ denote the convex set formed by taking the $(m-1)$-jets of all such $F$ at a given finite set $S \subset \mathbb{R}^n$. We provide an efficient algorithm to compute a convex polyhedron $\tilde{\Gamma}_f (S,M)$, such that $$ \Gamma_f (S,cM) \subset \tilde{\Gamma}_f (S,M) \subset \Gamma_f (S,CM), $ where $c$ and $C$ depend only on $m$ and $n$.

Keywords: Interpolation, jet, algorithm, Whitney extension theorem.

Fefferman Charles, Israel Arie: The Jet of an Interpolant on a Finite Set. Rev. Mat. Iberoam. 27 (2011), 355-360. doi: 10.4171/RMI/639