The aim of this paper is to construct a modied greedy algorithm applicable for an ill-posed function approximation problem in presence of data noise. This algorithm, coupled with a suitable stopping rule, can be interpreted as an iterative regularization method. We provide a detailed convergence analysis of the algorithm in presence of noise, and discuss optimal choices of parameters. As a consequence of this analysis, we also obtain results on the optimal choice of the network size in presence of noise.
Finally, we discuss the application of the modied greedy algorithm to sigmoidal neural networks and radial basis functions, and supplement the theoretical results by numerical experiments.

@Article{BH05,
  author       = {Burger, M. and Hofinger, A.},
  title        = {Greedy algorithms for neural network training with data noise},
  journal      = {Computing},
  volume       = {74},
  pages        = {1-22},
  year         = {2005},
  url          = \{/2005/BH05},
}