Skip to main content
SpringerLink
Log in

A lower bound for the number of nodes in the cubature formula for a centrally symmetric integral

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

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. G. G. Rasputin, “Some questions in the algebraic theory of cubature formulas,” Manuscript desposited at VINITI, No. 5272-B 87 (1987).

  2. B. Renschuch, Elementare und Praktische Idealtheorie, VEB Deutscher Verlag der Wissenschaften, Berlin (1976).

    Google Scholar 

  3. I. P. Mysovskikh, Interpolational Cubature Formulas [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  4. H. M. Möller, “Lower bounds for the number of nodes in cubature formulae,” in: Numerische Integration (Tagung, Math. Forschungsinst., Oberwolfach, 1978), Internat. Ser. Numer. Math., No. 45, Birkhauser, Basel (1979), pp. 221–230.

    Google Scholar 

  5. J.-J. Risler, “Une caractérisation des idéaux des variétés algébriques réeles,” C. R. Acad. Sci. Paris, Ser. A-B,271, No. 23, A1171-A1173 (1970).

    Google Scholar 

  6. H. M. Möller, “Kubaturformeln mit minimaler Knotenzahl,” Numer. Math.,25, No. 2, 185–200 (1976).

    Google Scholar 

  7. F. S. Macaulay, The Algebraic Theory of Modular Systems, Cambridge Univ. Press (1916).

  8. I. P. Mysovskikh, “On the calculation of integrals over the surface of the sphere,” Dokl. Akad. Nauk SSSR,235, No. 2, 269–272 (1977).

    Google Scholar 

  9. M. V. Noskov, “Cubature formulas for the approximate integration of periodic functions,” in: Metody Vychisl., No. 14, Leningrad State Univ. (1985), pp. 15–23.

  10. I. P. Mysovskikh, “On cubature formulas that are exact for trigonometric polynomials,” Dokl. Akad. Nauk SSSR,296, No. 1, 28–31 (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Arkhangel'sk Wood Technology Institute, USSR

    G. G. Rasputin

Authors
  1. G. G. Rasputin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 45, No. 5, pp. 70–75, May, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rasputin, G.G. A lower bound for the number of nodes in the cubature formula for a centrally symmetric integral. Mathematical Notes of the Academy of Sciences of the USSR 45, 396–400 (1989). https://doi.org/10.1007/BF01157934

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01157934

Keywords

Search

Navigation