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### The Jet of an Interpolant on a Finite Set

Charles Fefferman and Arie Israel
Source: Rev. Mat. Iberoamericana Volume 27, Number 1 (2011), 355-360.

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$. First Page: Primary Subjects: 49K24, 52A35 Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.rmi/1296828838 Mathematical Reviews number (MathSciNet): MR834355 Zentralblatt MATH identifier: 05883110 ### References Callahan, P.B. and Kosaraju, S.R.: A decomposition of multidimensional point sets with applications to$k$-nearest-neighbors and$n$-body potential fields. J. Assoc. Comput. Mach. 42 (1995), no. 1, 67-90. Mathematical Reviews (MathSciNet): MR1370371 Digital Object Identifier: doi:10.1145/200836.200853 Fefferman, C. and Klartag, B.: Fitting a$C^m$-smooth function to data. Part I, Ann. of Math. (2) 169 (2009), 315-346. Part II, Rev. Mat. Iberoam. 25 (2009), 49-273. Fefferman, C.: Fitting a$C^m\$-smooth function to data. III. Ann of Math. (2) 170 (2009), no. 1, 427-441.
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