Relaxing convergence conditions for Newton's method.
The classical Kantorovich theorem on Newton's method assumes that the first derivative of the operator involved satisfies a Lipschitz condition ∥Γ0[F′(x)-F′(y)]∥≤L∥x-y∥. In this paper, we weaken this condition, assuming that ∥Γ0[F′(x)-F′(x0)]∥≤ω(∥x-x0∥) for a given point x0. © 2000 Academic Pre...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2000 |
| País: | España |
| Institución: | Universidad de La Rioja (UR) |
| Repositorio: | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| OAI Identifier: | oai:portal.dialnet.es:doc/5bbc69f1b750603269e8242c |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc69f1b750603269e8242c |
| Access Level: | acceso abierto |
| Palabra clave: | Iterative processes Kantorovich conditions Newton's method |
| Sumario: | The classical Kantorovich theorem on Newton's method assumes that the first derivative of the operator involved satisfies a Lipschitz condition ∥Γ0[F′(x)-F′(y)]∥≤L∥x-y∥. In this paper, we weaken this condition, assuming that ∥Γ0[F′(x)-F′(x0)]∥≤ω(∥x-x0∥) for a given point x0. © 2000 Academic Press. |
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