Adaptive Approximation by Greedy Algorithms

This talk will discuss computational algorithms that deal with the
following general task: given a function f and a dictionary of functions
D in a Hilbert space, extract a linear combination of N functions in
D which approximates f at best. We shall review the properties of
existing algorithms, and focus on two of them which are computationally
simple and have optimal convergence properties. This work is
motivated by applications as various as data compression,
adaptive numerical simulation of PDE’s in large space
dimension, statistical learning theory.