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New and generalized convergence conditions for the Newton-Kantorovich method

Argyros I. K.

Journal of Applied Analysis

2003

Vol. 9, nr 2

287-299

We present new semilocal convergence theorems for Newton methods in a Banach space. Using earlier general conditions we find more precise error estimates on the distances involved using the majorant principle. Moreover we provide a better information on the location of the solution. In the special case of Newton's method under Lipschitz conditions we show that the famous Newton-Kantorovich hypothesis having gone unchallenged for a long time can be weakened under the same hypotheses/computational cost.