Pointwise and uniform approximation by multivariate neural network operators of the max-product type. (September 2016)

• Record Type: Journal Article
• Authors: Costarelli, Danilo; Vinti, Gianluca
• Is Part Of: Neural networks. Volume 81(2016)
• Page Start: 81
• Page End: 90
• Publication Date: 2016-09
• Subjects: Sigmoidal functions -- Multivariate neural networks operators -- Uniform approximation -- Order of approximation -- Max-product operators; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2016.06.002
• Languages: English
• ISSNs: 0893-6080

Abstract

Abstract: In this article, the theory of multivariate max-product neural network (NN) and quasi-interpolation operators has been introduced. Pointwise and uniform approximation results have been proved, together with estimates concerning the rate of convergence. At the end, several examples of sigmoidal activation functions have been provided.