, Volume 33, Issue 1, pp 51–64 | Cite as

Difference Newton-like methods under weak continuity conditions

  • T. J. Ypma
Contributed Papers


We give a local convergence analysis of difference Newton-like methods for solving the nonlinear equationF(x)=0, without assuming Lipschitz continuity of the derivativeF′. The results are obtained by regarding difference Newton-like methods as inexact Newton methods.

AMS Subject Classification


Key words

Nonlinear equations difference approximation Newton-like methods 

Newton-ähnliche Verfahren vom Differenztyp unter schwachen Stetigkeitsvoraussetzungen


Wir befassen uns mit einer Konvergenzanalyse für Newton-ähnliche Verfahren vom Differenztyp zur Lösung der nichtlinearen GleichungF(x)=0, ohne die Voraussetzung, daß die AbleitungF′ Lipschitz-stetig ist. Die Resultate entstehen daraus, daß wir Newton-ähnliche Verfahren vom Differenztyp als approximäre (inexact) Newton-Verfahren ansehen.


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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • T. J. Ypma
    • 1
  1. 1.Department of Applied MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa

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