# Fitting a Smooth Function to Data

 SHORT TALKS BY POSTDOCTORAL MEMBERS Topic: Fitting a Smooth Function to Data Speaker: Bo'az Klartag Affiliation: IAS Date: Tuesday, October 4 Time/Room: 4:00pm - 5:00pm/S-101

Suppose we are given a finite subset E in an n-dimensional real space, and a real valued function f defined on E. How to extend f to a C^m smooth function F, defined on the entire R^n, with C^m norm of the smallest possible order of magnitude? We exhibit algorithms for constructing such an extension function F. Let N be the cardinality of the set E. Our algorithm starts with analyzing the data using C N log N computer operations. Then, it is ready to answer queries: given any point x in R^n, the algorithm returns the value F(x) using C log N computer operations. Here C is a constant depending only on m and n. This is a joint work with C. Fefferman.