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Section B

On the convergence region of Newton's method under Hölder continuity conditions

Pages 317-326 | Received 18 Dec 2006, Accepted 24 Feb 2008, Published online: 12 Sep 2008
 

Abstract

We approximate a locally unique solution of an equation in a Banach space setting using Newton's method under Hölder continuity assumptions. Using more precise estimates on the distances involved than before [F. Cianciaruso and E. DePascale, Estimates of majorizing sequences in the Newton–Kantorovich method, Numer. Funct. Anal. Optim. 27(5 and 6) (2006), pp. 529–538], we show that the convergence region is extended with finer error estimates and the location of the solution is precise under the same computational cost.

2000 AMS Subject Classification :

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