On the Newton-Kantorovich hypothesis for solving equations

Authors:
Ioannis K. Argyros
Affiliations:
Department of Mathematical Sciences, Cameron University, Lawton, OK
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

Citing 3
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Abstract

The famous Newton-Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton's method to a solution of an equation in connection with the Lipschitz continuity of the Fréchet-derivative of the operator involved. Here using Lipschitz and center-Lipschitz conditions we show that the Newton-Kantorovich hypothesis can be weakened. The error bounds obtained under our semilocal convergence result are more precise than the corresponding ones given by the dominating Newton-Kantorovich theorem.