Iterative methods based on spline approximations to detect discontinuities from Fourier data

Authors:
Ana Gabriela Martínez;Alvaro Rodolfo De Pierro
Affiliations:
Applied Mathematics Department, University of Campinas, IMECC-UNICAMP, CP 6065, 13081-970, Campinas, Brazil;Applied Mathematics Department, University of Campinas, IMECC-UNICAMP, CP 6065, 13081-970, Campinas, Brazil
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

Recently, spline approximations have been proposed for the reconstruction of piecewise smooth functions from Fourier data. That approach makes possible to retrieve the functions from their Fourier coefficients for any given degree of accuracy when the discontinuity points are known. In this paper we present iterative methods based on those spline approximations, for several degrees, to find locations and amplitudes of the jumps of a piecewise smooth function, given its Fourier coefficients. We also present numerical experiments comparing with different previous approaches.