Fitting a smooth function to data

Charles Fefferman, Department of Mathematics, Princeton University

ABSTRACT: Fix positive integers m, n, and suppose we are given a large finite set of points in R^(n+1). How can we compute a C^m function F:R^n->R whose graph passes through (or close to) the given points, with the C^m norm of F (approximately) as small as possible? Approximately how small is the C^m norm of the best F? What if we are allowed to discard a few of the points as "outliers"? Can we then make the norm much smaller? Joint work with Bo'az Klartag.