Function approximation arises in many branches of applied mathematics and computer science, in particular in numerical analysis, in finite element theory and more recently in data sciences domain. From most common approximation we cite, polynomial, Chebychev and Fourier series approximations. In this work we establish some approximations of a continuous function by a series of activation functions. First, we deal with one and two dimensional cases. Then, we generalize the approximation to the multi dimensional case. Examples of applications of these approximations are: interpolation, numerical integration, finite element and neural network. Finally, we will present some numerical results of the examples above.

Source : oai:HAL:hal-02543988v5

Volume: Volume 32 - 2019 - 2021

Published on: April 30, 2021

Submitted on: May 11, 2020

Keywords: numerical integration,universal approximation theorem,neural network,Chebychev points,Runge's phenomenon,interpolation,Function approximation,neural network,Chebychev points,Runge's phenomenon,interpolation,Function approximation,éléments finis,intégation numérique,théorème universel d'appoximation,réseau neuronal,points de Cheby- chev,phénomène de Runge,Approximation d'une fonction,[MATH]Mathematics [math]

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