Computing

, Volume 33, Issue 1, pp 51–64

Difference Newton-like methods under weak continuity conditions

• T. J. Ypma
Contributed Papers

Abstract

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.

65H10

Key words

Nonlinear equations difference approximation Newton-like methods

Newton-ähnliche Verfahren vom Differenztyp unter schwachen Stetigkeitsvoraussetzungen

Zusammenfassung

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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