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Ukrainian Mathematical Journal

, Volume 47, Issue 9, pp 1479–1485 | Cite as

An approach to the investigation of optimal quadrature formulas for singular integrals with fixed singularity

  • M. Sh. Shabozov
Article

Abstract

For classes of functions given on the segment [0,1], we obtain optimal quadrature formulas for singular integrals with fixed singularity. The obtained results are extended to the case of two-dimensional integrals.

Keywords

Quadrature Formula Singular Integral Fixed Singularity Optimal Quadrature Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    B. G. Gabdulkhaev,Optimal Approximations of Solutions of Linear Problems [in Russian], Kazan University, Kazan (1980).Google Scholar
  2. 2.
    I. V. Boikov,Algorithms for Approximate Calculation of Singular Integrals Optimal with Respect to Accuracy [in Russian], Saratov University, Saratov (1983).Google Scholar
  3. 3.
    S. M. Nikol'skii,Quadrature Formulas [in Russian], Nauka, Moscow (1979).Google Scholar
  4. 4.
    N. P. Korneichuk, “Optimization of adaptive algorithms for reconstruction of monotone functions of the classH ω,”Ukr. Mat. Zh.,45, No 12, 1627–1634 (1993).Google Scholar
  5. 5.
    A. G. Sukharev,Minimax Algorithms in Problems of Numerical Analysis [in Russian], Nauka, Moscow (1989).Google Scholar
  6. 6.
    L. A. Onegov, “On the best quadrature formula for singular integrals with fixed singularity,”Izv. Vyssh. Uchebn. Zaved. Mat, No. 9, 76–79 (1981).Google Scholar
  7. 7.
    M. Sh. Shabozov, “Estimates of errors of cubature formulas which are exact for splines on some classes of functions of two variables,”Ukr. Mat. Zh.,31, No 1, 74–82 (1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • M. Sh. Shabozov
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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