The jet of an interpolant on a finite set (Q533392)

Summary: 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 \(\widetilde{\Gamma}_f (S,M)\), such that \[ \Gamma_f (S,cM)\subset \widetilde{\Gamma}_f (S,M)\subset \Gamma_f (S,CM), \] where \(c\) and \(C\) depend only on \(m\) and \(n\).