On the Gauss-Newton method for solving equations
We use a combination of the center-Lipschitz condition with the Lipschitz condition condition on the Frechet-derivative of the operator involved to provide a semilocal convergence analysis of the Gauss-Newton method to a solution of an equation. Using more precise estimates on the distances involved...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | Chile |
| Institución: | Agencia Nacional de Investigación y Desarrollo |
| Repositorio: | SciELO Chile |
| OAI Identifier: | oai:scielo:S0716-09172012000100002 |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000100002 |
| Access Level: | acceso abierto |
| Palabra clave: | Gauss-Newton method semilocal convergence Frechet- derivative Lipschitz/center-Lipschitz condition convergence domain |
| Sumario: | We use a combination of the center-Lipschitz condition with the Lipschitz condition condition on the Frechet-derivative of the operator involved to provide a semilocal convergence analysis of the Gauss-Newton method to a solution of an equation. Using more precise estimates on the distances involved, under weaker hypotheses, and under the same computational cost, we provide an analysis of the Gauss- Newton method with the following advantages over the corresponding results in [8]: larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location ofthe solution |
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