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Izv. RAN. Ser. Mat., 1998, Volume 62, Issue 1, Pages 21–58 (Mi izv182)  

This article is cited in 20 scientific papers (total in 20 papers)

The best accuracy of reconstruction of finitely smooth functions from their values at a given number of points

S. N. Kudryavtsev


Abstract: We find the order of the best accuracy of reconstruction of functions in the Nikolskii and Besov classes (along with their derivatives up to a certain order) from their values at a given number of points.

DOI: https://doi.org/10.4213/im182

Full text: PDF file (2183 kB)
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English version:
Izvestiya: Mathematics, 1998, 62:1, 19–53

Bibliographic databases:

MSC: 41A63, 41A46
Received: 06.02.1997

Citation: S. N. Kudryavtsev, “The best accuracy of reconstruction of finitely smooth functions from their values at a given number of points”, Izv. RAN. Ser. Mat., 62:1 (1998), 21–58; Izv. Math., 62:1 (1998), 19–53

Citation in format AMSBIB
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\by S.~N.~Kudryavtsev
\paper The best accuracy of reconstruction of finitely smooth functions from their values at a~given number of points
\jour Izv. RAN. Ser. Mat.
\yr 1998
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\pages 21--58
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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. N. Kudryavtsev, “The Stechkin problem for partial derivation operators on classes of finitely smooth functions”, Math. Notes, 67:1 (2000), 61–68  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Sh. Azhgaliev, N. Temirgaliev, “Informativeness of Linear Functionals”, Math. Notes, 73:6 (2003), 759–768  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. S. N. Kudryavtsev, “Approximation of the derivatives of finitely smooth functions belonging to non-isotropic classes”, Izv. Math., 68:1 (2004), 77–123  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Proc. Steklov Inst. Math., 248 (2005), 268–277  mathnet  mathscinet  zmath
    5. Fang G.S., Hickernell F.J., Li H., “Approximation on anisotropic Besov classes with mixed norms by standard information”, Journal of Complexity, 21:3 (2005), 294–313  crossref  mathscinet  zmath  isi  scopus
    6. Novak E., Triebel H., “Function spaces in Lipschitz domains and optimal rates of convergence for sampling”, Constructive Approximation, 23:3 (2006), 325–350  crossref  mathscinet  zmath  isi  scopus
    7. S. N. Kudryavtsev, “Approximation and reconstruction of the derivatives of functions satisfying mixed Hölder conditions”, Izv. Math., 71:5 (2007), 895–938  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. Vybiral J., “Sampling numbers and function spaces”, Journal of Complexity, 23:4–6 (2007), 773–792  crossref  mathscinet  zmath  isi  scopus
    9. Dinh Dũng, “Non-linear sampling recovery based on quasi-interpolant wavelet representations”, Adv Comput Math, 2008  crossref  mathscinet  isi  scopus
    10. Novak E. Wozniakowski H., “Tractability of Multivariate Problems, Vol 1: Linear Information”, Tractability of Multivariate Problems, Vol 1: Linear Information, Ems Tracts in Mathematics, 6, Eur. Math. Soc., 2008, 1–384  crossref  mathscinet  isi
    11. Gen Sun Fang, Li Qin Duan, “Optimal recovery on the classes of functions with bounded mixed derivative”, Acta Math Sinica, 25:2 (2009), 279  crossref  mathscinet  zmath  isi  scopus
    12. Dinh Dũng, “Optimal adaptive sampling recovery”, Adv Comput Math, 2009  crossref  isi  scopus
    13. Dinh Dũng, “B-spline quasi-interpolant representations and sampling recovery of functions with mixed smoothness”, Journal of Complexity, 2011  crossref  mathscinet  isi  scopus
    14. Yuan Xiuhua, Ye Peixin, “Monte Carlo Approximation and Integration for Sobolev Classes”, High Performance Networking, Computing, and Communication Systems, Communications in Computer and Information Science, 163, ed. Wu Y., Springer-Verlag Berlin, 2011, 103–110  crossref  isi  scopus
    15. Ye P., Li X., “Optimal Recovery for Some Infinitely Differentiable Periodic Functions”, Advanced Research on Material Engineering, Chemistry and Bioinformatics, Pts 1 and 2 (Mecb 2011), Advanced Materials Research, 282-283, no. Part 1,2, eds. Zhang H., Jin D., Trans Tech Publications Ltd, 2011, 240–243  crossref  isi  scopus
    16. P. Gonzalez-Vera, M. I. Stessin, “Joint Spectra of Toeplitz Operators and Optimal Recovery of Analytic Functions”, Constr Approx, 2012  crossref  mathscinet  zmath  isi  elib  scopus
    17. Dinh Dũng, “Continuous algorithms in adaptive sampling recovery”, Journal of Approximation Theory, 166 (2013), 136  crossref  mathscinet  zmath  isi  scopus
    18. Jan Vybíral, “Weak and quasi-polynomial tractability of approximation of infinitely differentiable functions”, Journal of Complexity, 2013  crossref  mathscinet  isi  scopus
    19. Heping Wang, Kai Wang, “Optimal recovery of Besov classes of generalized smoothness and Sobolev classes on the sphere”, Journal of Complexity, 2015  crossref  mathscinet  scopus
    20. Kuo F.Y., Plaskota L., Wasilkowski G.W., “Optimal Algorithms For Doubly Weighted Approximation of Univariate Functions”, J. Approx. Theory, 201 (2016), 30–47  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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