Paper Info
Title
Complete algebraic reconstruction of piecewise-smooth functions from Fourier data.
Abstract
In this paper we provide a reconstruction algorithm for piecewise-smooth functions with a priori known smoothness and a number of discontinuities, from their Fourier coefficients, possessing 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.
Year
DOI
Venue
2015
10.1090/S0025-5718-2015-02948-2
MATHEMATICS OF COMPUTATION
Keywords
Field
DocType
Fourier inversion,nonlinear approximation,piecewise-smooth functions,Eckhoff's conjecture,Eckhoff's method,Gibbs phenomenon
Gibbs phenomenon,Mathematical optimization,Algebraic number,Mathematical analysis,Fourier transform,Piecewise,Mathematics,Nonlinear approximation
Journal
Volume
Issue
ISSN
84
295
0025-5718
Citations 
PageRank 
References 
6
0.58
18
Authors
1
Name
Order
Citations
PageRank
Dmitry Batenkov1257.19