Interpolation by neural network operators activated by ramp functions |
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Authors: | Danilo Costarelli |
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Affiliation: | Dipartimento di Matematica e Fisica, Sezione di Matematica, “Roma Tre” University, 1, Largo S. Leonardo Murialdo, 00146 Rome, Italy |
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Abstract: | In this paper, a family of interpolation neural network operators are introduced. Here, ramp functions as well as sigmoidal functions generated by central B-splines are considered as activation functions. The interpolation properties of these operators are proved, together with a uniform approximation theorem with order, for continuous functions defined on bounded intervals. The relations with the theory of neural networks and with the theory of the generalized sampling operators are discussed. |
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Keywords: | Sigmoidal functions Neural network operators Interpolation Uniform approximation Order of approximation Ramp function |
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