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A note on Newton type iterative methods

Über einige Varianten des Newtonschen Iterationsverfahrens

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Abstract

Some particular rates of convergence, in the sense of Potra and Pták [4], are related to Newton type iterative methods which solve nonlinear operator equations in Banach spaces. This allows to obtain convergence conditions and a posteriori error estimates at the same time. The applicability of the estimates thus found is studied and their behaviour illustrated by numerical examples.

Zusammenfassung

Es wird ein Verfahren vorgestellt, das zugleich Konvergenzbedingungen und Fehlerschranken bei der Anwendung von Iterationsverfahren der Formx n+1=x n −A(x n)−1 F(x n) zur Lösung nichlinearer GleichungenF(x)=0 in Banachräumen zu bestimmen gestattet. Die Anwendung der Abschätzungen wird besprochen und an numerischen Beispielen erläutert.

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Moret, I. A note on Newton type iterative methods. Computing 33, 65–73 (1984). https://doi.org/10.1007/BF02243076

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AMS Subject Classification

  • 65J15

Key word

  • Interative methods
  • Newton's method