Complete Algebraic Reconstruction of Piecewise-Smooth Functions from Fourier Data
Numerical Analysis
2014-03-18 v2 Classical Analysis and ODEs
Abstract
In this paper we provide a reconstruction algorithm for piecewise-smooth functions with a-priori known smoothness and number of discontinuities, from their Fourier coefficients, posessing the maximal possible asymptotic rate of convergence -- including the positions of the discontinuities and the pointwise values of the function. This algorithm is a modification of our earlier method, which is in turn based on the algebraic method of K.Eckhoff proposed in the 1990s. The key ingredient of the new algorithm is to use a different set of Eckhoff's equations for reconstructing the location of each discontinuity. Instead of consecutive Fourier samples, we propose to use a "decimated" set which is evenly spread throughout the spectrum.
Keywords
Cite
@article{arxiv.1211.0680,
title = {Complete Algebraic Reconstruction of Piecewise-Smooth Functions from Fourier Data},
author = {Dmitry Batenkov},
journal= {arXiv preprint arXiv:1211.0680},
year = {2014}
}