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'...

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Detalles Bibliográficos
Autores: Amat, S. [0000-0002-9954-5240], Ezquerro, J.A. [0000-0001-8120-167X], Hernández-Verón, M.A. [0000-0001-5478-2958]
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
Descripción
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.