Skip to main content
SpringerLink
Log in

On the rate of convergence of some projection methods for linear operator equations

  • Published:
Ukrainian Mathematical Journal 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. L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces [in Russian], Fizmatgiz, Moscow (1959).

    Google Scholar 

  2. S. G. Mikhlin, The Problem of the Minimum of a Quadratic Functional [in Russian], Gostekhizdat, Moscow-Leningrad (1952).

    Google Scholar 

  3. S. G. Mikhlin, Variational Methods in Mathematical Physics [in Russian], Gostekhizdat, Moscow (1957).

    Google Scholar 

  4. S. G. Mikhlin, The Numerical Realization of Variational Methods [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  5. N. I. Pol'skii, “On the convergence of some approximate methods of analysis,” Ukr. Matem, Zh.,7, No. 1 (1955).

  6. N. I. Pol'skii, “Projection methods in applied mathematics,” Dokl. AN SSSR,143, No. 4 (1962).

  7. A. E. Martynyuk, “Some new applications of methods of Galerkin type,” Matem. Sb.,49 (91), No. 1 (1959).

  8. W. V. Petryshyn, “Direct and iterative methods for the solution of linear operator equations in Hilbert space,” Trans. Am. Math. Soc.,105 (1962).

  9. W. V. Petryshyn, “On a class of K-p.d. and non-K-p.d. operators and operator equations,” Jour. Math. Anal. and Applic.,10, No. 1 (1965).

  10. 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 

  11. A. V. Dzhishkariani, “On the method of Bubnov-Galerkin,” Zh. Vychisl. Matem. i Matem. Fiz.,7, No. 6 (1967).

  12. A. V. Dzhishkariani, “On least squares and Bubnov-Galerkin methods,” Zh. Vychisl. Matem. i Matem. Fiz.,8, No. 5 (1968).

  13. A. Yu. Luchka, “On the rate of convergence of residuals and errors to zero of the Bubnov-Galerkin and least squares methods,” Proceedings of a Seminar on Differential and Integral Equations [in Russian], Izd. Inst. Matem. AN UkrSSR, No. 1 (1969).

  14. A. Yu. Luchka, “Some remarks on the rate of convergence of the method of moments,” Proceedings of a seminar on Mathematical Safeguards for ÉTsVM and the Efficient Organization of Computational Processes [in Russian], Izd. Inst. Kibernetiki AN UkrSSR, No. 4 (1969).

  15. M. A. Krasnosel'skii, P. P. Zabreiko, E. I. Pystyl'nik, and P. E. Sobolevskii, Integral Operators in Spaces of Summable Functions [in Russian], Nauka, Moscow (1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, USSR

    A. Yu. Luchka

Authors
  1. A. Yu. Luchka
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 23, No. 3, pp. 307–317, May–June, 1971.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Luchka, A.Y. On the rate of convergence of some projection methods for linear operator equations. Ukr Math J 23, 259–267 (1971). https://doi.org/10.1007/BF01085349

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01085349

Keywords

Search

Navigation