Fourier series approximation of separable models

Authors:
U. Amato;A. Antoniadis;I. De Feis
Affiliations:
Istituto per le Applicazioni del Calcolo "Mauro Picone" - Sezione di Napoli CNR, Via Pietro Castellino 111, 80131 Napoli, Italy;LMC-IMAG, Universitè Joseph Fourier, BP 53, 38041 Grenoble Cedex 09, France;Istituto per le Applicazioni del Calcolo "Mauro Picone" - Sezione di Napoli CNR, Via Pietro Castellino 111, 80131 Napoli, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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Abstract

The approximation of a function affected by noise in several dimensions suffers from the so-called "curse of dimensionality". In this paper a Fourier series method based on regularization is developed both for uniform and random design when a restriction on the complexity of the curve such as additivity is considered in order to circumvent the problem. Optimal convergence theorems are stated and numerical experiments are shown on several test problems available in the literature together with comparisons with alternative methods.