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 $n$.