Skip to main content
SpringerLink
Log in

Interval forms of Newtons method

Intervallformen des Newtonschen Verfahrens

  • Published:
Computing Aims and scope Submit manuscript

Abstract

Improved forms of some interval Newton Methods are given. It is shown that certain intervals in the methods can be replaced by real numbers. This improves the convergence properties of the methods.

Zusammenfassung

Eine verbesserte Darstellung Newtonscher Intervall-Verfahren wird diskutiert. Es wird dabei gezeigt, daß man bestimmte Intervalle in den Verfahren durch reelle Zahlen ersetzen kann. Dadurch werden die Konvergenzeigenschaften der Verfahren verbessert.

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. Alefeld, G., Herzberger, J.: Einführung in die Intervallrechnung. Mannheim: Bibliographisches Institut 1974.

    Google Scholar 

  2. Hansen, E. R.: On Solving Systems of Equations Using Interval Arithmetic. Math. Comp.22, 374–384 (1968).

    Google Scholar 

  3. Hansen, E. R. (ed.): Topics in Interval Analysis. Oxford: Clarendon Press 1969.

    Google Scholar 

  4. Krawczyk, R.: Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken. Computing4, 187–201 (1969).

    Article  Google Scholar 

  5. Moore, R. E.: Interval Analysis. Prentice-Hall 1966.

  6. Moore, R. E.: A Test for Existence of Solutions to Nonlinear Systems. SIAM J. Num. Anal.14, 611–615 (1977).

    Article  Google Scholar 

  7. Nickel, K.: On the Newton Method in Interval Analysis. Mathematics Research Center Report 1136, University of Wisconsin, 1971.

Download references

Author information

Authors and Affiliations

  1. Department of Pure and Applied Mathematics, Washington State University, 99164, Pullman, WA, USA

    E. Hansen

Authors
  1. E. Hansen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hansen, E. Interval forms of Newtons method. Computing 20, 153–163 (1978). https://doi.org/10.1007/BF02252344

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02252344

Keywords

Search

Navigation