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Constructive Approximation of Discontinuous Functions by Neural Networks

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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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Authors and Affiliations

  1. Departamento de Matemática Aplicada, E.T.S.I. de Caminos, Universidad Politécnica de Madrid, Ciudad Universitaria s/n, 28040, Madrid, Spain

    B. Llanas, S. Lantarón & F. J. Sáinz

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  1. B. Llanas
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  2. S. Lantarón
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  3. F. J. Sáinz
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Correspondence to B. Llanas.

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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

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