## New thoughts on least-squares methods

- March 27, 2012
- 3:30 p.m.
- LeConte 412

## Abstract

Least squares methods are of common use when one needs to approximate a function based on its noiseless or noisy observation at n scattered points by a simpler function chosen in an m dimensional space with m less than n. Depending on the context, these points may be randomly drawn according to some distribution, or deterministically selected by the user. In this talk, I shall analyze the stability and approximation properties of least squares method. This analysis involves the relative size of m with respect to n as well as the spatial distribution of the samples. Applications will be given for high dimensional sparse polynomial approximation and approximation by plane waves.