Geodesic
A weaker affine covariant Newton–Mysovskikh theorem for solving equations
Ioannis K. Argyros1
1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A.
Applicationes Mathematicae, Tome 33 (2006) no. 3-4, pp. 355-363.

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

The Newton–Mysovskikh theorem provides sufficient conditions for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. It turns out that under weaker hypotheses and a more precise error analysis than before, weaker sufficient conditions can be obtained for the local as well as semilocal convergence of Newton's method. Error bounds on the distances involved as well as a larger radius of convergence are obtained. Some numerical examples are also provided.
DOI : 10.4064/am33-3-9
Keywords: newton mysovskikh theorem provides sufficient conditions semilocal convergence newtons method locally unique solution equation banach space setting turns out under weaker hypotheses precise error analysis before weaker sufficient conditions obtained local semilocal convergence newtons method error bounds distances involved larger radius convergence obtained numerical examples provided

Ioannis K. Argyros 1

1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, U.S.A. 
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Ioannis K. Argyros. A weaker affine covariant
 Newton–Mysovskikh theorem for
 solving equations. Applicationes Mathematicae, Tome 33 (2006) no. 3-4, pp. 355-363. doi : 10.4064/am33-3-9. http://geodesic.mathdoc.fr/articles/10.4064/am33-3-9/

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