Skip to main content
SpringerLink
Log in

Optimization of adaptive direct methods for the solution of operator equations in Hilbert space

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

Some general theorems on estimates of error of optimal adaptive direct methods of solution of operator equations of type II in Hilbert space are obtained.

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

Literature cited

  1. N. S. Bakhvalov, Numerical Methods [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  2. S. L. Sobolev, Equations of Mathematical Physics [in Russian], Hostekhizdat, Moscow (1960).

    Google Scholar 

  3. S. V. Pereverzev, “On optimal methods for specifying information in the solution of integral equations with differentiable kernels,” Ukr. Mat. Zh.,38, No. 1, 55–63 (1986).

    Google Scholar 

  4. S. V. Pereverzev, “On the optimization of methods of approximation of solutions of integral equations with differentiable kernels,” Sib. Mat. Zh.,28, No. 3, 173–183 (1987).

    Google Scholar 

  5. N. S. Kurpel', Projection-iterative Methods for the Solution of Operator Equations [in Russian], Nauk, Dumka, Kiev (1968).

    Google Scholar 

  6. L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  7. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  8. V. M. Tikhomirov, Some Problems in Approximation Theory [in Russian], Izdat. Mosk. Univ., Moscow (1976).

    Google Scholar 

  9. A. I. Grebennikov, “The spline-approximation method and its application,” Authors Abstract of Doctoral Dissertation, Physicomathematical Sciences, Novosibirsk (1989).

    Google Scholar 

  10. A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).

    Google Scholar 

  11. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press (1970).

  12. G. Valnikko, A. Pedas, and P. Uba, Methods of Solution of Weakly Singular Integral Equations [in Russian], Tartus. Univ. (1984).

Download references

Author information

Authors and Affiliations

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

    S. G. Solodkii

Authors
  1. S. G. Solodkii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 1, pp. 95–102, January, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Solodkii, S.G. Optimization of adaptive direct methods for the solution of operator equations in Hilbert space. Ukr Math J 42, 85–92 (1990). https://doi.org/10.1007/BF01066368

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01066368

Keywords

Search

Navigation