Abstract
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.
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Llanas, B., Lantarón, S. & Sáinz, F.J. Constructive Approximation of Discontinuous Functions by Neural Networks. Neural Process Lett 27, 209–226 (2008). https://doi.org/10.1007/s11063-007-9070-9
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DOI: https://doi.org/10.1007/s11063-007-9070-9