Semilocal Convergence of the Secant Method under Mild Convergence Conditions of Differentiability

In this work, we obtain a semilocal convergence result for the secant method in Banach spaces under mild convergence conditions. We consider a condition for divided differences which generalizes those usual ones, i.e., Lipschitz continuous and Hölder continuous conditions. Also, we obtain a result f...

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Detalhes bibliográficos
Autores: Hernández, M.A. [0000-0001-5478-2958], Rubio, M.J. [0000-0002-8765-4060]
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2002
País:España
Recursos:Universidad de La Rioja (UR)
Repositorio:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc69f3b750603269e82450
Acesso em linha:https://investigacion.unirioja.es/documentos/5bbc69f3b750603269e82450
Access Level:acceso abierto
Palavra-chave:Boundary value problems
Recurrence relations
The secant method
Descrição
Resumo:In this work, we obtain a semilocal convergence result for the secant method in Banach spaces under mild convergence conditions. We consider a condition for divided differences which generalizes those usual ones, i.e., Lipschitz continuous and Hölder continuous conditions. Also, we obtain a result for uniqueness of solutions. © 2002 Elsevier Science Ltd. All rights reserved.