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Dokl. Akad. Nauk SSSR, 1963, Volume 148, Number 5, Pages 1042–1045 (Mi dan27586)  

This article is cited in 27 scientific papers (total in 27 papers)


Quadrature and interpolation formulas for tensor products of certain classes of functions

S. A. Smolyak

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Presented: . . 
Received: 25.07.1962

Citation: S. A. Smolyak, “Quadrature and interpolation formulas for tensor products of certain classes of functions”, Dokl. Akad. Nauk SSSR, 148:5 (1963), 1042–1045

Citation in format AMSBIB
\by S.~A.~Smolyak
\paper Quadrature and interpolation formulas for tensor products of certain classes of functions
\jour Dokl. Akad. Nauk SSSR
\yr 1963
\vol 148
\issue 5
\pages 1042--1045

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    This publication is cited in the following articles:
    1. A. G. Vitushkin, G. M. Henkin, “Linear superpositions of functions”, Russian Math. Surveys, 22:1 (1967), 77–125  mathnet  crossref  mathscinet  zmath
    2. V. N. Temlyakov, “Approximate recovery of periodic functions of several variables”, Math. USSR-Sb., 56:1 (1987), 249–261  mathnet  crossref  mathscinet  zmath
    3. E. D. Nursultanov, N. T. Tleukhanova, “Approximate computation of integrals for functions in $W_p^\alpha[0,1]^n$”, Russian Math. Surveys, 55:6 (2000), 1165–1167  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. E. D. Nursultanov, N. T. Tleukhanova, “Quadrature formulae for classes of functions of low smoothness”, Sb. Math., 194:10 (2003), 1559–1584  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Sh. Azhgaliev, N. Temirgaliev, “Informativeness of Linear Functionals”, Math. Notes, 73:6 (2003), 759–768  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. N. T. Tleukhanova, “Interpolation Formula for Functions of Several Variables”, Math. Notes, 74:1 (2003), 151–153  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. A. G. Vitushkin, “On Hilbert's thirteenth problem and related questions”, Russian Math. Surveys, 59:1 (2004), 11–25  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    8. N. N. Dobrovolskii, “Otklonenie dvumernykh setok Smolyaka”, Chebyshevskii sb., 8:1 (2007), 110–152  mathnet  mathscinet  zmath
    9. L. P. Bocharova, N. M. Dobrovolskii, I. Yu. Rebrova, “Pyatdesyat let teoretiko-chislovomu metodu v priblizhennom analize: problemy i dostizheniya”, Chebyshevskii sb., 8:4 (2007), 4–49  mathnet
    10. O. V. Kiseleva, “O zadache Korobova dlya modifitsirovannykh setok Smolyaka”, Chebyshevskii sb., 8:4 (2007), 50–104  mathnet
    11. M. A. Romanov, “O pogreshnosti sluchainykh kvadraturnykh formul na nekotorykh klassakh funktsii”, Dalnevost. matem. zhurn., 7:1-2 (2007), 91–100  mathnet
    12. Sh. U. Azhgaliev, “Discretization of the Solutions of the Heat Equation”, Math. Notes, 82:2 (2007), 153–158  mathnet  crossref  crossref  mathscinet  isi  elib
    13. M. A. Romanov, “On the Error of Multidimensional Quadrature Formulas for Certain Classes of Functions”, Math. Notes, 85:3 (2009), 420–425  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. N. Zh. Nauryzbaev, N. Temirgaliev, “On the Order of Discrepancy of the Smolyak Grid”, Math. Notes, 85:6 (2009), 897–901  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. N. Temirgaliev, S. S. Kudaibergenov, A. A. Shomanova, “An application of tensor products of functionals in problems of numerical integration”, Izv. Math., 73:2 (2009), 393–434  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. G. W. Wasilkowski, H. Woźniakowski, “A survey of average case complexity for linear multivariate problems”, Russian Math. (Iz. VUZ), 53:4 (2009), 1–14  mathnet  crossref  mathscinet
    17. N. Temirgaliev, S. S. Kudaibergenov, A. A. Shomanova, “Applications of Smolyak quadrature formulas to the numerical integration of Fourier coefficients and in function recovery problems”, Russian Math. (Iz. VUZ), 54:3 (2010), 45–62  mathnet  crossref  mathscinet  elib
    18. L. P. Dobrovolskaya, M. N. Dobrovolskii, N. M. Dobrovolskii, N. N. Dobrovolskii, “Giperbolicheskie dzeta-funktsii setok i reshetok i vychislenie optimalnykh koeffitsientov”, Chebyshevskii sb., 13:4 (2012), 4–107  mathnet
    19. S. S. Kudaibergenov, S. G. Sabitova, “Discretization of solutions to Poissons equation in the Korobov class”, Comput. Math. Math. Phys., 53:7 (2013), 896–907  mathnet  crossref  crossref  mathscinet  isi  elib
    20. E. D. Nursultanov, N. T. Tleukhanova, “On reconstruction of multiplicative transformations of functions in anisotropic spaces”, Siberian Math. J., 55:3 (2014), 482–497  mathnet  crossref  mathscinet  isi  elib  elib
    21. E. A. Bailov, M. B. Sikhov, N. Temirgaliev, “General algorithm for the numerical integration of functions of several variables”, Comput. Math. Math. Phys., 54:7 (2014), 1061–1078  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    22. N. Temirgaliyev, N. Zh. Nauryzbayev, A. A. Shomanova, “Approximative possibilities of computational aggregates of the “Smolyak type” with Dirichlet, Fejer and Vallée-Poussin kernels in the scale of Ul'yanov classes”, Russian Math. (Iz. VUZ), 59:7 (2015), 67–72  mathnet  crossref
    23. S. S. Demidov, E. A. Morozova, V. N. Chubarikov, I. Yu. Rebrova, I. N. Balaba, N. N. Dobrovolskii, N. M. Dobrovolskii, L. P. Dobrovolskaya, A. V. Rodionov, O. A. Pikhtilkova, “Teoretiko-chislovoi metod v priblizhennom analize”, Chebyshevskii sb., 18:4 (2017), 6–85  mathnet  crossref  elib
    24. N. Zh. Nauryzbaev, A. A. Shomanova, N. Temirgaliyev, “On some special effects in theory on numerical integration and functions recovery”, Russian Math. (Iz. VUZ), 62:3 (2018), 84–88  mathnet  crossref  isi
    25. I. Yu. Rebrova, V. N. Chubarikov, N. N. Dobrovolskii, M. N. Dobrovolskii, N. M. Dobrovolskii, “O klassicheskikh teoretiko-chislovykh setkakh”, Chebyshevskii sb., 19:4 (2018), 118–176  mathnet  crossref  elib
    26. N. Temirgaliev, S. S. Kudaibergenov, N. Zh. Nauryzbaev, “Poryadkovo tochnoe vychislenie integralov ot proizvedenii funktsii metodom tenzornykh proizvedenii funktsionalov”, Izv. vuzov. Matem., 2019, no. 11, 94–99  mathnet  crossref
    27. N. N. Dobrovolskii, D. V. Gorbachev, V. I. Ivanov, “O trekhmernykh setkakh Smolyaka I”, Chebyshevskii sb., 20:3 (2019), 193–219  mathnet  crossref
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