2012/11/04 by Dmitry Batenkov, Batenkov, Dmitry · 2 citations
Engineering · Mathematics · #65D15 #65T40 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1211.0680
openalex publication_date 2012/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.