Majorizing sequences for Newton's method from initial value problems

Authors:
J. A. Ezquerro;D. González;M. A. Hernández
Affiliations:
-;-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

Citing 5
Cited 0

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Abstract

The most restrictive condition used by Kantorovich for proving the semilocal convergence of Newton's method in Banach spaces is relaxed in this paper, providing we can guarantee the semilocal convergence in situations that Kantorovich cannot. To achieve this, we use Kantorovich's technique based on majorizing sequences, but our majorizing sequences are obtained differently, by solving initial value problems.