{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:51:27Z","timestamp":1776797487422,"version":"3.51.2"},"reference-count":40,"publisher":"American Mathematical Society (AMS)","issue":"295","license":[{"start":{"date-parts":[[2016,2,19]],"date-time":"2016-02-19T00:00:00Z","timestamp":1455840000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>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\u2014including 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.\u00a0Eckhoff proposed in the 1990s. The key ingredient of the new algorithm is to use a different set of Eckhoff\u2019s equations for reconstructing the location of each discontinuity. Instead of consecutive Fourier samples, we propose to use a \u201cdecimated\u201d set which is evenly spread throughout the spectrum.<\/p>","DOI":"10.1090\/s0025-5718-2015-02948-2","type":"journal-article","created":{"date-parts":[[2015,2,19]],"date-time":"2015-02-19T10:10:31Z","timestamp":1424340631000},"page":"2329-2350","source":"Crossref","is-referenced-by-count":19,"title":["Complete algebraic reconstruction of piecewise-smooth functions from Fourier data"],"prefix":"10.1090","volume":"84","author":[{"given":"Dmitry","family":"Batenkov","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2015,2,19]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1137\/130908221","article-title":"A stability barrier for reconstructions from Fourier samples","volume":"52","author":"Adcock, Ben","year":"2014","journal-title":"SIAM J. Numer. 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