Fitting a Cm-smooth function to data I

Charles Fefferman, Bo'az Klartag

Research output: Contribution to journalArticlepeer-review

Abstract

Suppose we are given a finite subset E ⊂ R{double struck} n and a function f: E → R{double struck}. How to extend f to a Cm function F: R{double struck} n → R{double struck} with Cm 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 Cm norm. The running time of our algorithms is never more than CN log N, where N is the cardinality of E and C is a constant depending only on m and n.

Original languageEnglish
Pages (from-to)315-346
Number of pages32
JournalAnnals of Mathematics
Volume169
Issue number1
DOIs
StatePublished - 2009
Externally publishedYes

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