Tampos, A. L.Lope, J. E. C.Hesthaven, Jan S.2013-11-122013-11-122013-11-122012https://infoscience.epfl.ch/handle/20.500.14299/96958In this paper, we present a singularity-based resolution of the Gibbs phenomenon that obstructs the reconstruction of a function with jump discontinuities by a truncated Chebyshev series or a Padé-Chebyshev approximation. We tackle the more difficult case where the jump locations are not known. The identification of unknown singularities is carried out using a Padi-Chebyshev approximation. Numerical examples to illustrate the method are provided, including an application on postprocessing computational data corrupted by the Gibbs phenomenon.Chebyshev seriesComputational dataDiscontinuous functionsFunction reconstructionGibbs phenomenaIdentification of unknownsJump discontinuitiesNumerical examplePade-Chebyshev approximationChebyshev approximationtext::journal::journal article::research article