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A semilocal convergence result for Newton’s method under generalized conditions of Kantorovich |
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| Authors: | J.A. Ezquerro,D. Gonzá lez,M.A. Herná ndez-Veró n |
| Affiliation: | University of La Rioja, Department of Mathematics and Computation, C/Luis de Ulloa s/n, 26004 Logroño, Spain |
| Abstract: | From Kantorovich’s theory we establish a general semilocal convergence result for Newton’s method based fundamentally on a generalization required to the second derivative of the operator involved. As a consequence, we obtain a modification of the domain of starting points for Newton’s method and improve the a priori error estimates. Finally, we illustrate our study with an application to a special case of conservative problems. |
| Keywords: | Newton&rsquo s method Semilocal convergence The Newton&ndash Kantorovich theorem Majorizing sequence A priori error estimates Conservative problem |
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