Fitting a Cm-smooth function to data I

Charles Fefferman

doi:10.4007/annals.2009.169.315

Fitting a Cm-smooth function to data I

2009-01-01

51

OA

AI

DOI：10.4007/annals.2009.169.315

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Suppose we are given a finite subset E subset of R-n and a function f : E -> R. How to extend f to a C-m function F : R-n -> 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 CN log N, where N is the cardinality of E and C is a constant depending only on m and n.

Keyword:

WHITNEYS EXTENSION PROBLEM

CLOSED-SETS

LINEAR-OPERATORS

THEOREM

Fitting a Cm-smooth function to data I

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