Skip to main content
SpringerLink
Log in

On the radius of convergence of Newton’s method under average mild differentiability conditions

  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

We provide a local convergence analysis for Newton’s method under mild differentiability conditions on the operator involved in a Banach space setting. In particular we show that under the same hypotheses and computational cost but using more precise estimates we can provide a larger convergence radius and finer error bounds on the distances involved than before (Huang in Comput. Math. Math. 42:247–251, 2004; Rheinboldt in Banach Ctr. Publ. 3:129–142, 1977; Wang in IMA J. Numer. Anal. 20:123–134, 2000). Some numerical examples are used to further justify the usage of our results over the earlier ones mentioned above.

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

References

  1. Argyros, I.K.: On Newton’s method under mild differentiability conditions and applications. Appl. Math. Comput. 102, 177–183 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  2. Argyros, I.K.: A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space. J. Math. Anal. Appl. 298, 374–397 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. Argyros, I.K.: Newton Methods. Nova Science, New York (2005)

    MATH  Google Scholar 

  4. Huang, Z.: The convergence ball of Newton’s method and the uniqueness ball of equations under Hölder-type continuous derivatives. Comput. Math. Math. 42, 247–251 (2004)

    Google Scholar 

  5. Kantorovich, L.V., Akilov, G.P.: Functional Analysis in Normed Spaces. Pergamon, Oxford (1982)

    Google Scholar 

  6. Rheinboldt, W.C.: An adaptive continuation process for solving systems of nonlinear equations. Banach Ctr. Publ. 3, 129–142 (1977)

    MathSciNet  Google Scholar 

  7. Wang, X.: Convergence of Newton’s method and uniqueness of the solution of equations in Banach space. IMA J. Numer. Anal. 20, 123–134 (2000)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

Authors
  1. Ioannis K. Argyros
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ioannis K. Argyros.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Argyros, I.K. On the radius of convergence of Newton’s method under average mild differentiability conditions. J. Appl. Math. Comput. 29, 429–435 (2009). https://doi.org/10.1007/s12190-008-0143-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-008-0143-3

Keywords

Mathematics Subject Classification (2000)

Search

Navigation