Max-product neural network and quasi-interpolation operators activated by sigmoidal functions

The max-product neural network (NN) and quasi-interpolation (QI) operators are here introduced and studied. The density functions considered as kernels for the above operators are generated by certain finite linear combination of sigmoidal functions, and from them inherit very useful approximation p...

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Bibliographic Details
Published in:Journal of approximation theory Vol. 209; pp. 1 - 22
Main Authors: Costarelli, Danilo, Vinti, Gianluca
Format: Journal Article
Language:English
Published: Elsevier Inc 01.09.2016
Subjects:
Max-product operators
Neural networks operators
Order of approximation
Sigmoidal functions
Uniform approximation
41A25
Max-product operators
41A30
47A58
Uniform approximation
Sigmoidal functions
41A05
Neural networks operators
Order of approximation
ISSN:0021-9045, 1096-0430
Online Access:Get full text
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Summary:The max-product neural network (NN) and quasi-interpolation (QI) operators are here introduced and studied. The density functions considered as kernels for the above operators are generated by certain finite linear combination of sigmoidal functions, and from them inherit very useful approximation properties. The convergence and the rate of approximation for the max-product NN and QI operators are studied. Estimates involving the modulus of continuity of the functions being approximated have been derived. Several examples are provided together with some applications and graphical representations. The relations with the general theory of neural networks and sampling operators are discussed in detail.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2016.05.001