Skip to main content
SpringerLink
Log in

Problem of the construction of optimal quadratures for functions of several variables

  • Published:
Cybernetics Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. A. G. Sukharev, “On an approach for the investigation of the efficiency of quadrature formulas,” Kibernetika, No. 6, 94–99 (1981).

    Google Scholar 

  2. S. M. Nikol'skii, Quadrature Formulas [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  3. N. P. Korneichuk, “Best cubature formulas for certain classes of functions of several variables,” Mat. Zametki,3, No. 5, 565–576 (1968).

    Google Scholar 

  4. Maung Chzho N'yun and I. F. Sharygin, “Optimal cubature formulas on the classes D 12 ,c and D 1s ,l 1,” Vopr. Vychisl. Prikl. Mat., No. 5, 22–27 (1971).

    Google Scholar 

  5. V. F. Babenko, “An asymptotically accurate estimation of the remainder of best cubature formulas for certain classes of functions,” Mat. Zametki,19, No. 3, 313–322 (1976).

    Google Scholar 

  6. V. F. Babenko, “An accurate asymptotics for the remainders of weighted cubature formulas which are optimal for certain classes of functions,” Mat. Zametki,20, No. 4, 589–595 (1976).

    Google Scholar 

  7. V. F. Babenko, “On the optimal error bound for cubature formulas on certain classes of continuous functions,” Anal. Math.,3, No. 1, 3–9 (1977).

    Google Scholar 

  8. A. G. Sukharev, The Optimal Search for an Extremum [in Russian], Mosk. Univ., Moscow (1975).

    Google Scholar 

  9. H. Coxeter, “The classification of zonohedra by means of projective diagrams,” J. Math. Pure Appl.,41, No. 2, 137–156 (1962).

    Google Scholar 

  10. S. S. Ryshkov and E. P. Batanovskii, “C-types of n-dimensional lattices and five-dimensional positive parallelohedra (with application to the theory of coverings),” Trudy Mat. Inst. Akad. Nauk SSSR, Vol. 137, Moscow (1976).

  11. C. A. Rogers, “A note on coverings,” Mathematika,4, 1–6 (1957).

    Google Scholar 

  12. C. A. Rogers, Packing and Covering, Cambridge Univ. Press, New York (1964).

    Google Scholar 

  13. A. N. Kolmogorov and V. M. Tikhomirov, “ε-entropy and ε-capacity of sets in function spaces,” Usp. Mat. Nauk,14, No. 2, 3–86 (1959).

    Google Scholar 

  14. N. S. Bakhvalov, “On the approximate computation of multiple integrals,” Vestn. Mosk. Gos. Univ., Ser. Mat., Mekh., Astr., Fiz., Khim., No. 4, 3–18 (1959).

    Google Scholar 

  15. S. L. Sobolev, Introduction into the Theory of Cubature Formulas [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  16. S. S. Ryshkov, “The effectuation of a method of Davenport in the theory of coverings,” Dokl. Akad. Nauk SSSR,175, No. 2, 303–305 (1967).

    Google Scholar 

Download references

Authors
  1. A. G. Sukharev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Kibernetika, No. 1, pp. 7–11, January–February, 1982.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sukharev, A.G. Problem of the construction of optimal quadratures for functions of several variables. Cybern Syst Anal 18, 8–14 (1982). https://doi.org/10.1007/BF01078044

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01078044

Keywords

Search

Navigation