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Approximation of a function and its derivative with a neural network

Cardaliaguet, Pierre; Euvrard, Guillaume (1992), Approximation of a function and its derivative with a neural network, Neural Networks, 5, 2, p. 207-220. http://dx.doi.org/10.1016/S0893-6080(05)80020-6

Type
Article accepté pour publication ou publié
Date
1992
Journal name
Neural Networks
Volume
5
Number
2
Publisher
Elsevier
Pages
207-220
Publication identifier
Metadata
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Author(s)
Cardaliaguet, Pierre
Euvrard, Guillaume
Abstract (EN)
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.
Subjects / Keywords
Feedforward neural networks; Functions approximation; Interpolation; Bell-shaped functions; Squashing functions; Robustness with respect to noise; Implicit function; Control