CONVERGENCE OF NEWTON'S METHOD UNDER THE GAMMA CONDITION
We provide a semilocal as well as a local convergence analysis ofNewton's method using the gamma condition [1], [10], [11]. Usingmore precise majorizing sequences than before [4], [8]-[11] and underat least as weak hypotheses, we provide in the semilocal case: finererror bounds on the distances...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2006 |
| País: | Chile |
| Institución: | CONICYT Chile |
| Repositorio: | SciELO Chile |
| OAI Identifier: | oai:scielo:S0716-09172006000300006 |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172006000300006 |
| Access Level: | acceso abierto |
| Palabra clave: | Banach space Newton's method local/semilocalconvergence Newton-Kantorovich theorem Fréchet derivative majorizingsequence radius of convergence gamma condition analyticoperator |
| Sumario: | We provide a semilocal as well as a local convergence analysis ofNewton's method using the gamma condition [1], [10], [11]. Usingmore precise majorizing sequences than before [4], [8]-[11] and underat least as weak hypotheses, we provide in the semilocal case: finererror bounds on the distances involved and an at least as precise informationon the location of the solution; in the local case: a largerradius of convergence |
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