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Ukrainian Mathematical Journal

, Volume 46, Issue 9, pp 1327–1335 | Cite as

Optimal rates of convergence of some iterative approximation methods for the solution of fredholm equations in spaces of periodic analytic functions

  • S. V. Pereverzev
  • M. Askarov
Article
  • 20 Downloads

Abstract

We consider some classes of Fredholm equations with integral operators acting in spaces of periodic analytic functions. For these classes, we establish the exact order of the optimal rates of convergence for some versions of the method of iterative projections and KP methods.

Keywords

Analytic Function Approximation Method Integral Operator Optimal Rate Iterative Approximation 
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.
    W. V. Lovitt,Linear Integral Equations, McGraw-Hill, New York (1924).Google Scholar
  2. 2.
    S. N. Zaliznyak, Yu. I. Mel'nik, and Yu. K. Podlipenko, “On approximate solutions of integral equations in potential theory,”Ukr. Mat. Zh.,33, No. 3, 382–391 (1981).Google Scholar
  3. 3.
    V. M. Tikhomirov,Some Problems in the Theory of Approximation [in Russian], Moscow University, Moscow (1976).Google Scholar
  4. 4.
    A. Yu. Luchka,Method of Iterative Projections for the Solution of Differential and Integral Equations [in Russian], Naukova Dumka, Kiev (1980).Google Scholar
  5. 5.
    V. I. Lebedev, “On the iterative KP-method,”Zh. Vych. Mat. Mat. Fit.,7, No. 6, 137–148 (1967).Google Scholar
  6. 6.
    G. I. Marchuk and V. I. Lebedev,Numerical Methods in the Theory of Neutron Transfer [in Russian], Atomizdat, Moscow (1971).Google Scholar
  7. 7.
    M. A. Krasnosel'skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, and V. Ya. Stetsenko,Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).Google Scholar
  8. 8.
    S. V. Pereverzev and M. A. Sinenko, “On the optimal convergence rate of the KP-method and its generalizations,”Zh. Vych. Mat. Mat. Fiz.,31, No. 10, 1452–1460 (1991).Google Scholar
  9. 9.
    S. V. Pereverzev, “On the optimal choice of basis functions in the solution of integral equations by the method of iterative projections,” in:Theory of Approximation and Related Problems in Analysis and Topology [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1987), pp. 82–87.Google Scholar
  10. 10.
    M. A. Sinenko, “On the relationship between the method of iterative projections and the KP-method for equations of the second kind,” in:Contemporary Problems in the Theory of Approximation and Complex Analysis, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1990), pp. 113–122.Google Scholar
  11. 11.
    S. G. Solodkii, “Optimization of adaptive direct methods for the solution of operator equations in Hubert spaces,”Ukr. Mat. Zh.,42, No. 1, 96–101 (1990).Google Scholar
  12. 12.
    N. P. Korneichuk,Extremal Problems in the Theory of Approximation [in Russian], Nauka, Moscow (1976).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • S. V. Pereverzev
    • 1
  • M. Askarov
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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