Accurate reconstruction of discontinuous functions using the singular pade-chebyshev method
In 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 PadÃ©-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.
Keywords: Chebyshev series ; Computational data ; Discontinuous functions ; Function reconstruction ; Gibbs phenomena ; Identification of unknowns ; Jump discontinuities ; Numerical example ; Pade-Chebyshev approximation ; Chebyshev approximation
Record created on 2013-11-12, modified on 2016-08-09