Semilocal convergence of a k-step iterative process and its application for solving a special kind of conservative problems

[EN] In this paper, we analyze the semilocal convergence of k-steps Newton's method with frozen first derivative in Banach spaces. The method reaches order of convergence k + 1. By imposing only the assumption that the Fr,chet derivative satisfies the Lipschitz continuity, we define appropr...

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Detalles Bibliográficos
Autores: Hernández-Verón, Miguel Angel, Martínez Molada, Eulalia|||0000-0003-2869-4334, Teruel-Ferragud, Carles
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/105894
Acceso en línea:https://riunet.upv.es/handle/10251/105894
Access Level:acceso abierto
Palabra clave:Nonlinear equations
Order of convergence
Iterative methods
Semilocal convergence
Conservative systems
MATEMATICA APLICADA
Descripción
Sumario:[EN] In this paper, we analyze the semilocal convergence of k-steps Newton's method with frozen first derivative in Banach spaces. The method reaches order of convergence k + 1. By imposing only the assumption that the Fr,chet derivative satisfies the Lipschitz continuity, we define appropriate recurrence relations for obtaining the domains of convergence and uniqueness. We also define the accessibility regions for this iterative process in order to guarantee the semilocal convergence and perform a complete study of their efficiency. Our final aim is to apply these theoretical results to solve a special kind of conservative systems.