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Matematicheskie Zametki, 2018, Volume 103, Issue 5, paper published in the English version journal (Mi mzm12094)  
This article is cited in 2 scientific papers (total in 2 papers)

Papers published in the English version of the journal

Exponential Convergence of an Approximation Problem for Infinitely Differentiable Multivariate Functions

Yongping Liua, Guiqiao Xub, Jie Zhanga

a School of Mathematical Sciences, Beijing Normal University, Beijing, People's Republic of China
b School of Mathematical Sciences, Tianjin Normal University, Tianjin, People's Republic of China
Citations (2)
Abstract: We study approximation problems for infinitely differentiable multivariate functions in the worst-case setting. Using a series of information-based algorithms as approximation tools, in which each algorithm is constructed by performing finitely many standard information operations, we prove that the $L_\infty$-approximation problem is exponentially convergent. As a corollary, we show that the corresponding integral problem is exponentially convergent as well.
Keywords: infinitely differentiable function class, standard information, worst-case setting.
Funding agency Grant number
National Natural Science Foundation of China 11471043
11671271
National Science Foundation Beijing Office 1172004
This work was supported in part by The National Natural Science Foundation of China under grants 11471043 and 11671271 and, in part, by the Beijing Municipal Natural Science Foundation under grant 1172004.
Received: 08.11.2017
Revised: 25.03.2018
English version:
Mathematical Notes, 2018, Volume 103, Issue 5, Pages 769–779
DOI: https://doi.org/10.1134/S0001434618050097
Bibliographic databases:
Document Type: Article
Language: English
Citation: Yongping Liu, Guiqiao Xu, Jie Zhang, “Exponential Convergence of an Approximation Problem for Infinitely Differentiable Multivariate Functions”, Math. Notes, 103:5 (2018), 769–779
Citation in format AMSBIB
\Bibitem{LiuGuiJie18}
\by Yongping~Liu, Guiqiao Xu, Jie Zhang
\paper Exponential Convergence of an Approximation Problem
for Infinitely Differentiable Multivariate Functions
\jour Math. Notes
\yr 2018
\vol 103
\issue 5
\pages 769--779
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\crossref{https://doi.org/10.1134/S0001434618050097}
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\elib{https://elibrary.ru/item.asp?id=32823052}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85049142079}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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