The aim of this paper is to construct a modified greedy algorithm applicable for an ill-posed function approximation problem in presence of data noise. We provide a detailed convergence analysis of the algorithm in presence of noise, and discuss the choice of the iteration parameters. This yields a stopping rule for which the corresponding algorithm is a regularization method with convergence rates in
L2 and under weak additional assumptions also in Sobolev-spaces of positive order.
Finally, we discuss the application of the modified greedy algorithm to sigmoidal neural networks and radial basis functions, and supplement the theoretical results by numerical experiments.
AMS Subject Classifications: 41A46 - 47A52 - 41A65 - 92B20
Keywords Greedy approximation - data noise - neural networks - regularization - training