Approximation of inverse operators by a new family of high-order iterative methods
SUMMARY: The main goal of this paper is to approximate inverse operators by high-order Newton-type methods with the important feature of not using inverse operators. We analyse the semilocal convergence, the speed of convergence, and the efficiency of these methods. We determine that Chebyshev'...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| 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/5bbc69f6b750603269e82485 |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc69f6b750603269e82485 |
| Access Level: | acceso abierto |
| Palabra clave: | Boundary value problem Heat equation Inverse operator Iterative method Order of convergence Semilocal convergence |
| Sumario: | SUMMARY: The main goal of this paper is to approximate inverse operators by high-order Newton-type methods with the important feature of not using inverse operators. We analyse the semilocal convergence, the speed of convergence, and the efficiency of these methods. We determine that Chebyshev's method is the most efficient method and test it on two problems: one associated to the heat equation and the other one to a boundary value problem. We consider examples with matrices that are close to be singular and/or are badly conditioned. We check the robustness and the stability of the methods by considering situations with many steps and noised data. © 2013 John Wiley & Sons, Ltd. |
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