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Uspekhi Mat. Nauk, 1950, Volume 5, Issue 2(36), Pages 165–177 (Mi umn8416)  

This article is cited in 31 scientific papers (total in 32 papers)

Scientific notes and problems

Concerning estimation for approximate quadrature formulas

S. M. Nikol'skii

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Citation: S. M. Nikol'skii, “Concerning estimation for approximate quadrature formulas”, Uspekhi Mat. Nauk, 5:2(36) (1950), 165–177

Citation in format AMSBIB
\by S.~M.~Nikol'skii
\paper Concerning estimation for approximate quadrature formulas
\jour Uspekhi Mat. Nauk
\yr 1950
\vol 5
\issue 2(36)
\pages 165--177

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    This publication is cited in the following articles:
    1. N. P. Korneichuk, N. E. Lushpai, “Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation”, Math. USSR-Izv., 3:6 (1969), 1335–1355  mathnet  crossref  mathscinet  zmath
    2. V. P. Motornyi, “On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions”, Math. USSR-Izv., 8:3 (1974), 591–620  mathnet  crossref  mathscinet  zmath
    3. A. A. Zhensykbaev, “Monosplines of minimal norm and the best quadrature formulae”, Russian Math. Surveys, 36:4 (1981), 121–180  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. A. Zhensykbaev, “Extremality of monosplines of minimal deficiency”, Math. USSR-Izv., 21:3 (1983), 461–482  mathnet  crossref  mathscinet  zmath
    5. S. M. Nikol'skii, “Aleksandrov and Kolmogorov in Dnepropetrovsk”, Russian Math. Surveys, 38:4 (1983), 41–55  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. M. A. Chahkiev, “Exponential polynomials of least deviation from zero and optimal quadrature formulas”, Math. USSR-Sb., 48:1 (1984), 273–285  mathnet  crossref  mathscinet  zmath
    7. N. P. Korneichuk, “S. M. Nikol'skii and the development of research on approximation theory in the USSR”, Russian Math. Surveys, 40:5 (1985), 83–156  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. I. V. Boykov, “Optimal cubature formulae for computing many-dimensional integrals of functions in the class $Q_{r,\gamma}(\Omega,1)$”, U.S.S.R. Comput. Math. Math. Phys., 30:4 (1990), 110–117  mathnet  crossref  mathscinet  zmath
    9. A. V. Gavrilov, “O kvadraturnykh formulakh, nailuchshikh v gilbertovom prostranstve s vosproizvodyaschim yadrom”, Sib. zhurn. vychisl. matem., 1:4 (1998), 313–320  mathnet  zmath
    10. S. A. Telyakovskii, “S. M. Nikol'skii's Works on the Theory of Approximation of Functions”, Proc. Steklov Inst. Math., 232 (2001), 13–18  mathnet  mathscinet  zmath
    11. O. V. Besov, V. A. Sadovnichii, S. A. Telyakovskii, “On the scientific work of S. M. Nikol'skii”, Russian Math. Surveys, 60:6 (2005), 1005–1020  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. B. D. Boyanov, “Optimal quadrature formulae”, Russian Math. Surveys, 60:6 (2005), 1035–1055  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. “The List of S.M. Nikol'skii's Works”, Proc. Steklov Inst. Math., 248 (2005), 2–20  mathnet  mathscinet  zmath
    14. M. K. Kerimov, “On the 100th birthday of Academician Sergei Mikhailovich Nikol'skii”, Comput. Math. Math. Phys., 46:3 (2006), 345–353  mathnet  crossref  mathscinet  elib
    15. S. P. Sidorov, “Optimal Recovery of Linear Functionals on Sets of Finite Dimension”, Math. Notes, 84:4 (2008), 561–567  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. Shadimetov Kh.M., Hayotov A.R., “Optimal quadrature formulas with positive coefficients in L-2((m)) (0,1) space”, Journal of Computational and Applied Mathematics, 235:5 (2011), 1114–1128  crossref  isi
    17. Babenko V.F., Borodachov S.V., Skorokhodov D.S., “Optimal cubature formulas for tensor products of certain classes of functions”, J Complexity, 27:6 (2011), 519–530  crossref  isi
    18. Hayotov A.R., Milovanovic G.V., Shadimetov Kh.M., “On an optimal quadrature formula in the sense of Sard”, Numer Algorithms, 57:4 (2011), 487–510  crossref  isi
    19. Babenko V.F., Borodachov S.V., Skorokhodov D.S., “Construction of Optimal Cubature Formulas Related to Computer Tomography”, Constr Approx, 33:3 (2011), 313–330  crossref  isi
    20. Shadimetov Kh.M., Hayotov A.R., Azamov S.S., “Optimal Quadrature Formula in K-2(P-2) Space”, Appl. Numer. Math., 62:12 (2012), 1893–1909  crossref  isi
    21. Shadimetov Kh.M. Hayotov A.R. Nuraliev F.A., “On an Optimal Quadrature Formula in Sobolev Space l-2((M))(0,1)”, J. Comput. Appl. Math., 243 (2013), 91–112  crossref  isi
    22. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On the best methods for recovering derivatives in Sobolev classes”, Izv. Math., 78:6 (2014), 1138–1157  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    23. Shadimetov Kh.M., Hayotov A.R., “Optimal Quadrature Formulas in the Sense of Sard in Space”, Calcolo, 51:2 (2014), 211–243  crossref  isi
    24. Hayotov A.R., Milovanovic G.V., Shadimetov Kh.M., “Optimal Quadrature Formula in the Sense of Sard in K-2(P-3) Space”, Publ. Inst. Math.-Beograd, 95:109 (2014), 29–47  crossref  isi
    25. S. A. Unuchek, “O vosstanovlenii operatora razdelennoi raznosti po netochno zadannomu preobrazovaniyu Fure”, Vladikavk. matem. zhurn., 17:3 (2015), 84–92  mathnet
    26. Hayotov A.R. Milovanovic G.V. Shadimetov Kh.M., “Optimal Quadratures in the Sense of Sard in a Hilbert Space”, 259, 2015, 637–653  crossref  isi
    27. Shadimetov Kh.M. Hayotov A.R. Nuraliev F.A., “Optimal Quadrature Formulas of Euler-Maclaurin Type”, 276, 2016, 340–355  crossref  isi
    28. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Exactness and optimality of methods for recovering functions from their spectrum”, Proc. Steklov Inst. Math., 293 (2016), 194–208  mathnet  crossref  crossref  mathscinet  isi  elib
    29. I. V. Boykov, “Optimal cubature formulas for calculation of multidimensional integrals in weighted Sobolev spaces”, Siberian Math. J., 57:3 (2016), 425–441  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    30. E. A. Balova, K. Yu. Osipenko, “Optimal Recovery Methods for Solutions of the Dirichlet Problem that are Exact on Subspaces of Spherical Harmonics”, Math. Notes, 104:6 (2018), 781–788  mathnet  crossref  crossref  mathscinet  isi  elib
    31. N. Temirgaliev, A. Zh. Zhubanysheva, “Computational (Numerical) diameter in a context of general theory of a recovery”, Russian Math. (Iz. VUZ), 63:1 (2019), 79–86  mathnet  crossref  crossref  isi
    32. A. R. Hayotov, F. A. Nuraliev, R. I. Parovik, Kh. M. Shadimetov, “Euler-Maclaurin type optimal formulas for numerical integration in Sobolev space”, Vestnik KRAUNTs. Fiz.-mat. nauki, 32:3 (2020), 75–101  mathnet  crossref
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