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- Title
Accurate Reconstruction of Discontinuous Functions Using the Singular Padé-Chebyshev Method.
- Authors
Tampos, Arnel L.; Lope, Jose Ernie C.; Hesthaven, Jan S.
- Abstract
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 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 Padé-Chebyshev approximation. Numerical examples to illustrate the method are provided, including an application on postprocessing computational data corrupted by the Gibbs phenomenon.
- Subjects
DISCONTINUOUS functions; MATHEMATICAL singularities; CHEBYSHEV series; APPROXIMATION theory; GIBBS phenomenon; DATA corruption; NUMERICAL analysis
- Publication
IAENG International Journal of Applied Mathematics, 2012, Vol 42, Issue 4, p242
- ISSN
1992-9978
- Publication type
Article