Approximation of a function and its derivative with a neural network

This paper deals with the approximation of both a function and its derivative by feedforward neural networks. We propose an explicit formula of approximation which is noise resistant and can be easily modified with the patterns. We apply these results to approach a function defined implicitly, which...

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Veröffentlicht in:	Neural networks 1992, Vol.5 (2), p.207-220
Hauptverfasser:	Cardaliaguet, Pierre, Euvrard, Guillaume
Format:	Artikel
Sprache:	eng
Schlagworte:	Approximations and expansions Bell-shaped functions Control Exact sciences and technology Feedforward neural networks Functions approximation Implicit function Interpolation Mathematical analysis Mathematics Robustness with respect to noise Sciences and techniques of general use Squashing functions
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Beschreibung
Zusammenfassung:	This paper deals with the approximation of both a function and its derivative by feedforward neural networks. We propose an explicit formula of approximation which is noise resistant and can be easily modified with the patterns. We apply these results to approach a function defined implicitly, which is useful in control theory.
ISSN:	0893-6080 1879-2782
DOI:	10.1016/S0893-6080(05)80020-6