On the R-order of convergence of Newton's method under mild differentiability conditions

Authors:
J. A. Ezquerro;M. A. Hernández
Affiliations:
Department of Mathematics and Computation, University of La Rioja, Logroño, Spain;Department of Mathematics and Computation, University of La Rioja, Logroño, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 2
Cited 4

A method for finding sharp error bounds for newton's method under the kantorovic assumptions

Numerische Mathematik
The Newton method for operators with Hölder continuous first derivative

Journal of Optimization Theory and Applications

New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems

Journal of Complexity
Weaker conditions for the convergence of Newton's method

Journal of Complexity
Majorizing sequences for iterative procedures in Banach spaces

Journal of Complexity
Estimating upper bounds on the limit points of majorizing sequences for Newton's method

Numerical Algorithms

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Abstract

A new technique is used instead of the classical majorant principle to analyze the R-order of convergence of the Newton process when more general conditions than the Kantorovich ones are considered.