Skip to main content
Log in

Some approximate methods of solving operator equations

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. B. A. Vertgeim, “Theorems on the convergence of Newton's method,” Nauchnye Trudy Permskogo Plotitekhnicheskogo Instituta, No. 7, 3–28 (1960).

    Google Scholar 

  2. B. A. Vertgeim, “Some methods of approximate solution of nonlinear functional equations in Banach spaces,” Uspekhi Matem. Nauk,12, No. 1, 166–169 (1957).

    Google Scholar 

  3. B. A. Vertgeim, “Conditions for applying Newton's method,” Dokl. Akad. Nauk SSSR,110, No. 5, 719–722 (1956).

    Google Scholar 

  4. B. A. Vertgeim, “Some conditions of convergence of Newton's method and application of the method to the solution of systems of equations,” Nauchnye Trudy Molotovskogo Gornogo Instituta, 142–153 (1956).

  5. I. A. Kusakin, “The majorant principle and the Newton-Kantorovich method with nondifferentiable operators,” Trudy Seminara po Functsional'nomu Analizu (Voronezhskii Universitet),10, 31–43 (1968).

    Google Scholar 

  6. L. V. Kantorovich and G. P. Akolov, Functional Analysis in Normed Spaces [in Russian], Fizmatgiz, Moscow (1959).

    Google Scholar 

  7. I. O. Kusakin, “Conversion of some methods of approximate solution of operator equations,” Dopovidi AN UkrSSR, No. 7, 830–834 (1965).

    Google Scholar 

  8. 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 

  9. J. E. Dennis, “On the Kantorovich hypothesis for Newton's method,” SIAM J. Numer. Analysis,6, No. 3, 493–507 (1969).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 13, No. 2, pp. 384–396, March–April, 1972.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Okinshevich, I.N. Some approximate methods of solving operator equations. Sib Math J 13, 266–274 (1972). https://doi.org/10.1007/BF00971614

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00971614

Keywords

Navigation