Abstract
We consider modifications of the interval Newton method which combine two ideas: Reusing the same evaluation of the Jacobian several (says) times and approximately solving the Newton equation by some ‘linear’ iterative process. We show in particular that theR-order of these methods may becomes+1. We illustrate our results by a numerical example.
Zusammenfassung
Wir betrachten Modifikationen des Intervall-Newton-Verfahrens, welche zwei Ansätze miteinander verbinden: Mehrfache (z.B.s-fache) Verwendung derselben Auswertung der Jacobi-Matrix und näherungsweise Lösung der Newton-Gleichung mit einem „linearen” Iterationsprozeß. Insbesondere zeigen wir, daß dieR-Ordnung dieser Verfahrens+1 werden kann. Wir illustrieren unsere Ergebnisse an einem numerischen Beispiel.
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Frommer, A., Mayer, G. Efficient methods for enclosing solutions of systems of nonlinear equations. Computing 44, 221–235 (1990). https://doi.org/10.1007/BF02262218
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DOI: https://doi.org/10.1007/BF02262218