Constructive approximation of discontinuous functions by neural networks
In this paper, we give a constructive proof that a real, piecewise continuous function can be almost uniformly approximated by single hidden-layer feedforward neural networks (SLFNNs). The construction procedure avoids the Gibbs phenomenon. Computer experiments show that the resulting approximant is much more accurate than SLFNNs trained by gradient descent.
constructive approximation approximation of discontinuous functions neural networks piecewise continuous functions gibbs phenomenon