On inverse methods for the resolution of the Gibbs phenomenon

Authors:
R. Pasquetti
Affiliations:
Department of Mathematics, Lab. J.A. Dieudonné, UMR CNRS 6621, Université de Nice-Sophia Antipolis, Parc Valrose, Nice 06108, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

When Fourier expansions, or more generally spectral methods, are used for the representation of nonsmooth functions, then one has to face the so-called Gibbs phenomenon. Considerable progresses have been made these last years to overcome the Gibbs phenomenon, using direct or inverse approaches, both in the discrete or continuous framework. A discrete inverse method for the global or local reconstruction of a non-smooth function starting from its oscillating (trigonometric) polynomial interpolant is introduced and both its capabilities and limits are emphasized.