On the Accessibility of Newton’s Method under a Hölder Condition on the First Derivative

On the Accessibility of Newton’s Method under a Hölder Condition on the First Derivative

We see how we can improve the accessibility of Newton's method for approximating a solution of a nonlinear equation in Banach spaces when a center Hölder condition on the first derivative is used to prove its semi-local convergence.

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Veröffentlicht in:Algorithms 2015-09, Vol.8 (3), p.514-528
Hauptverfasser: Ezquerro, José, Hernández-Verón, Miguel
Format: Artikel
Sprache:eng
Schlagworte:
Accessibility
Approximation
Convergence
Derivatives
domain of parameters
Mathematical analysis
Newton methods
Newton’s method
Nonlinear equations
nonlinear system
Partial differential equations
recurrence relations
semi-local convergence
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Beschreibung
Zusammenfassung:We see how we can improve the accessibility of Newton's method for approximating a solution of a nonlinear equation in Banach spaces when a center Hölder condition on the first derivative is used to prove its semi-local convergence.
ISSN:1999-4893
1999-4893
DOI:10.3390/a8030514