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.