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.
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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Ypma, T.J. Difference Newton-like methods under weak continuity conditions. Computing 33, 51–64 (1984). https://doi.org/10.1007/BF02243075
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DOI: https://doi.org/10.1007/BF02243075