Geodesic
Approximation by perturbed neural network operators
George A. Anastassiou1
1 Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A.
Applicationes Mathematicae, Tome 42 (2015) no. 1, pp. 57-81.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

This article deals with the determination of the rate of convergence to the unit of each of three newly introduced perturbed normalized neural network operators of one hidden layer. These are given through the modulus of continuity of the function involved or its high order derivative that appears in the right-hand side of the associated Jackson type inequalities. The activation function is very general, in particular it can derive from any sigmoid or bell-shaped function. The right-hand sides of our convergence inequalities do not depend on the activation function. The sample functionals are of Stancu, Kantorovich or quadrature types. We give applications for the first derivative of the function involved.
DOI : 10.4064/am42-1-5
Keywords: article deals determination rate convergence unit each three newly introduced perturbed normalized neural network operators hidden layer these given through modulus continuity function involved its high order derivative appears right hand side associated jackson type inequalities activation function general particular derive sigmoid bell shaped function right hand sides convergence inequalities depend activation function sample functionals stancu kantorovich quadrature types applications first derivative function involved

George A. Anastassiou 1

1 Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A. 
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George A. Anastassiou. Approximation by perturbed
 neural network operators. Applicationes Mathematicae, Tome 42 (2015) no. 1, pp. 57-81. doi : 10.4064/am42-1-5. http://geodesic.mathdoc.fr/articles/10.4064/am42-1-5/

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