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Approximation with activation functions and applications

Abstract : 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.
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Submitted on : Friday, April 30, 2021 - 11:55:21 AM
Last modification on : Wednesday, August 31, 2022 - 12:14:23 PM


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Radhia Bessi. Approximation with activation functions and applications. Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, 2021, Volume 32 - 2019 - 2021 (32), ⟨10.46298/arima.6464⟩. ⟨hal-02543988v5⟩



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