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Journal of Applied Analysis 9 (2003), No. 2, 287--299
Copyright Heldermann Verlag 2003
New and Generalized Convergence Conditions for the Newton-Kantorovich Method
Ioannis K. Argyros
Dept. of Mathematics, Cameron University, Lawton, OK 73505, U.S.A.,
ioannisa@cameron.edu
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.
Keywords: Newton's method, Banach space, majorant method, Newton-Kantorovich theorem/hypothesis,
Frechet-derivative.
MSC 2000: 65H10, 47H17, 49M15.
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