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Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 4, Pages 247–253 (Mi timm1370)  

This article is cited in 1 scientific paper (total in 1 paper)

Constructive sparse trigonometric approximations of functions with small mixed smoothness

S. A. Stasyuk

Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev

Abstract: Exact order bounds are obtained for the best $m$-term trigonometric approximation (in the integral metric) of periodic functions with small mixed smoothness from classes close to Nikol'skii-Besov type classes. The obtained bounds differ (under identical constraints on the smoothness) from the corresponding bounds of the best $m$-term trigonometric approximation of Besov classes of mixed smoothness established by A.S. Romanyuk. The upper bound is realized by a constructive method based on a greedy algorithm.

Keywords: nonlinear approximation, sparse approximation, mixed smoothness, order bounds.

Funding Agency Grant Number
European Union's Seventh Framework Programme 295164


DOI: https://doi.org/10.21538/0134-4889-2016-22-4-247-253

Full text: PDF file (179 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.518
MSC: 42A10, 42B10, 42B35
Received: 24.08.2016

Citation: S. A. Stasyuk, “Constructive sparse trigonometric approximations of functions with small mixed smoothness”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 4, 2016, 247–253

Citation in format AMSBIB
\Bibitem{Sta16}
\by S.~A.~Stasyuk
\paper Constructive sparse trigonometric approximations of functions with small mixed smoothness
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 4
\pages 247--253
\mathnet{http://mi.mathnet.ru/timm1370}
\crossref{https://doi.org/10.21538/0134-4889-2016-22-4-247-253}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3590938}
\elib{https://elibrary.ru/item.asp?id=27350142}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Stasyuk, “Razrezhennoe trigonometricheskoe priblizhenie klassov Besova funktsii s maloi smeshannoi gladkostyu”, Tr. IMM UrO RAN, 23, no. 3, 2017, 244–252  mathnet  crossref  elib
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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