title: Pointwise and uniform approximation by multivariate neural network operators of the max-product type.
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.
authors.affiliation: Department of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy. Electronic address: danilo.costarelli@unipg.it.
authors.forename: Danilo
authors.initials: D
authors.lastname: Costarelli
authors.affiliation: Department of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy. Electronic address: gianluca.vinti@unipg.it.
authors.forename: Gianluca
authors.initials: G
authors.lastname: Vinti
mesh_terms: D000465:Algorithms; D015999:Multivariate Analysis; D016571:Neural Networks, Computer
keywords: Max-product operators; Multivariate neural networks operators; Order of approximation; Sigmoidal functions; Uniform approximation