Skip to main content
SpringerLink
Log in

Optimization of the iterative process for the construction of a regularized solution of an operator equation of the first kind

  • II. Methods of Solution of Inverse Problems and Computer Techniques
  • Published:
Computational Mathematics and Modeling Aims and scope Submit manuscript

Abstract

An iterative process is proposed for constructing the solution of an equation of the first kind using known iterative methods and the Taylor series expansion of the regularized solution. Convergence of the process is proved. For the simple iteration method, the process is shown to be optimal by the number of operations.

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. A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution of Ill-Posed Problems [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  2. V. A. Morozov, "On regularizing families of operators," in: Computational Methods and Programming [in Russian], No. 8, Moscow State Univ. (1967), pp. 68–95.

  3. A. V. Kryanev, "Iterative method of solution of ill-posed problems," Zh. Vychisl. Mat. Mat. Fiz.,14, No. 1, 25–35 (1974).

    Google Scholar 

  4. A. A. Samarskii, An Introduction to Numerical Methods [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  5. V. I. Gordonova and V. A. Morozov, "Numerical parameter choosing algorithms in the regularization method," Zh. Vychisl. Mat. Mat. Fiz.,13, No. 3, 539–545 (1973).

    Google Scholar 

  6. V. I. Starostenko and S. M. Oganesyan, "Regularizing iteration processes," in: Methods of Solution of Ill-Posed Problems and Their Applications, Proc. All-Union School-Seminar, Noorus, 1982 [in Russian], Izd. VTs SO AN SSSR, Novosibirsk (1982), pp. 119–128.

    Google Scholar 

  7. J. Ortega and W. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York (1970).

    Google Scholar 

Download references

Authors
  1. P. N. Zaikin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. D. Merekalova
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 74–80, 1985.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zaikin, P.N., Merekalova, N.D. Optimization of the iterative process for the construction of a regularized solution of an operator equation of the first kind. Comput Math Model 1, 39–42 (1990). https://doi.org/10.1007/BF01128309

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01128309

Keywords

Search

Navigation