Geodesic
Fitting a $C^m$-smooth function to data, I
Charles Fefferman1 ; Bo'az Klartag2
1 Department of Mathematics<br/>Princeton University<br/>Princeton, NJ 08544<br/>United States
2 School of Mathematical Sciences<br/>Tel Aviv University<br/>Tel Aviv 69978<br/>Israel
Annals of mathematics, Tome 169 (2009) no. 1, pp. 315-346.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Suppose we are given a finite subset $E \subset \mathbb{R}^n$ and a function $f: E \rightarrow \mathbb{R}$. How to extend $f$ to a $C^m$ function $F: \mathbb{R}^n \rightarrow \mathbb{R}$ with $C^m$ norm of the smallest possible order of magnitude? In this paper and in [20] we tackle this question from the perspective of theoretical computer science. We exhibit algorithms for constructing such an extension function $F$, and for computing the order of magnitude of its $C^m$ norm. The running time of our algorithms is never more than $C N \log N$, where $N$ is the cardinality of $E$ and $C$ is a constant depending only on $m$ and $n$.
DOI : 10.4007/annals.2009.169.315

Charles Fefferman 1 ; Bo'az Klartag 2

1 Department of Mathematics<br/>Princeton University<br/>Princeton, NJ 08544<br/>United States
2 School of Mathematical Sciences<br/>Tel Aviv University<br/>Tel Aviv 69978<br/>Israel 
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Charles Fefferman; Bo'az Klartag. Fitting a $C^m$-smooth function to data, I. Annals of mathematics, Tome 169 (2009) no. 1, pp. 315-346. doi : 10.4007/annals.2009.169.315. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.169.315/

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