Geodesic
On the gap between the semilocal convergence domains of two Newton methods
Ioannis K. Argyros1
1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A.
Applicationes Mathematicae, Tome 34 (2007) no. 2, pp. 193-204.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We answer a question posed by Cianciaruso and De Pascale: What is the exact size of the gap between the semilocal convergence domains of the Newton and the modified Newton method? In particular, is it possible to close it? Our answer is yes in some cases. Using some ideas of ours and more precise error estimates we provide a semilocal convergence analysis for both methods with the following advantages over earlier approaches: weaker hypotheses; finer error bounds on the distances involved, and at least as precise information on the location of the solution; and a smaller gap between the two methods.
DOI : 10.4064/am34-2-4
Keywords: answer question posed cianciaruso pascale what exact size gap between semilocal convergence domains newton modified newton method particular possible close answer yes cases using ideas ours precise error estimates provide semilocal convergence analysis methods following advantages earlier approaches weaker hypotheses finer error bounds distances involved least precise information location solution smaller gap between methods

Ioannis K. Argyros 1

1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A. 
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Ioannis K. Argyros. On the gap between the semilocal
 convergence domains of two Newton methods. Applicationes Mathematicae, Tome 34 (2007) no. 2, pp. 193-204. doi : 10.4064/am34-2-4. http://geodesic.mathdoc.fr/articles/10.4064/am34-2-4/

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