Skip to main content
SpringerLink
Log in

On optimization of weight quadrature formulas

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We obtain asymptotically optimal quadrature formulas on the classH ω[-1, 1] for an arbitrary continuous weight function which is positive on [-1, 1] almost everywhere and for a wide class of moduli of continuity ω(t).

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

Similar content being viewed by others

References

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

    Google Scholar 

  2. G. K. Lebed', “On quadrature formulas with the lowest estimate of a remainder for some classes of functions,”Mat. Zametki,3, No. 5, 577–586 (1968).

    Google Scholar 

  3. B. F. Babenko, “Asymptotically exact estimate of the remainder of the best cubature formulas for some classes of functions,”Mat. Zametki,19, No. 3, 313–322 (1976).

    Google Scholar 

  4. V. P. Motornyi, “Investigation of the problem of optimization of quadrature formulas by Dnepropetrovsk mathematicians,”Ukr. Mat. Zh.,42, No. 1, 18–33 (1990).

    Google Scholar 

  5. V. A. Zorich,Mathematical Analysis [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  6. S. B. Stechkin, “One optimization problem,” in:Numerize Methoden der Approximations Theorie, Birkhaüser, Basel-Stuttgart (1972), pp. 205–208.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dnepropetrovsk University, Dnepropetrovsk

    V. F. Babenko

Authors
  1. V. F. Babenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 8, pp. 1011–1021, August, 1995.

This work was financially supported by the Ukrainian State Committee on Science and Technology.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Babenko, V.F. On optimization of weight quadrature formulas. Ukr Math J 47, 1157–1168 (1995). https://doi.org/10.1007/BF01057706

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01057706

Keywords

Search

Navigation