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Uspekhi Mat. Nauk, 2005, Volume 60, Issue 6(366), Pages 33–52 (Mi umn1675)  

This article is cited in 13 scientific papers (total in 13 papers)

Optimal quadrature formulae

B. D. Boyanov


Abstract: In this survey we consider results and open problems related to two major ideas in the theory of optimal quadrature formulae: the ideas of Gauss and Kolmogorov.

DOI: https://doi.org/10.4213/rm1675

Full text: PDF file (345 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2005, 60:6, 1035–1055

Bibliographic databases:

UDC: 517.5
MSC: Primary 41A55; Secondary 65D32, 31B30, 65D07
Received: 24.08.2005

Citation: B. D. Boyanov, “Optimal quadrature formulae”, Uspekhi Mat. Nauk, 60:6(366) (2005), 33–52; Russian Math. Surveys, 60:6 (2005), 1035–1055

Citation in format AMSBIB
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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. 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  mathscinet  zmath  isi
    2. V.F. Babenko, S.V. Borodachov, D.S. Skorokhodov, “Optimal cubature formulas for tensor products of certain classes of functions”, Journal of Complexity, 27:6 (2011), 519  crossref  mathscinet  zmath  isi
    3. 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  mathscinet  zmath  isi
    4. 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  mathscinet  zmath  isi
    5. 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  mathscinet  zmath  isi
    6. 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  mathscinet  zmath  isi
    7. Shadimetov Kh.M., Hayotov A.R., “Optimal Quadrature Formulas in the Sense of Sard in Space”, Calcolo, 51:2 (2014), 211–243  crossref  mathscinet  zmath  isi
    8. 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  mathscinet  zmath  isi
    9. 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  mathscinet  zmath  isi
    10. Shadimetov Kh.M., Hayotov A.R., Nuraliev F.A., “Optimal Quadrature Formulas of Euler-Maclaurin Type”, 276, 2016, 340–355  crossref  mathscinet  isi
    11. Babenko V.F. Babenko V.V. Polishchuk M.V., “On the Optimal Recovery of Integrals of Set-Valued Functions”, Ukr. Math. J., 67:9 (2016), 1306–1315  crossref  mathscinet  zmath  isi  elib  scopus
    12. Boltaev N.D., Hayotov A.R., Shadimetov Kh.M., “Construction of optimal quadrature formulas for Fourier coefficients in Sobolev space L 2 ( m ) ( 0 , 1 ) $L_{2}^{(m)}(0,1)$”, Numer. Algorithms, 74:2 (2017), 307–336  crossref  mathscinet  zmath  isi  scopus
    13. Kholmat M. Shadimetov, Farhod A. Nuraliev, “Optimal formulas of numerical integration with derivatives in Sobolev space”, Zhurn. SFU. Ser. Matem. i fiz., 11:6 (2018), 764–775  mathnet  crossref
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