A Uniparametric Family of Iterative Processes for Solving Non-Differentiable Equations

In this work we study a class of secant-like iterations for solving nonlinear equations in Banach spaces. We consider a condition for divided differences which generalizes the usual ones, i.e., Lipschitz and Hölder continuous conditions. A semilocal convergence result is obtained for nondifferentiab...

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Detalhes bibliográficos
Autores: Hernández, M.A. [0000-0001-5478-2958], Rubio, M.J. [0000-0002-8765-4060]
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2002
País:España
Recursos:Universidad de La Rioja (UR)
Repositório:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc69f4b750603269e82467
Acesso em linha:https://investigacion.unirioja.es/documentos/5bbc69f4b750603269e82467
Access Level:Acceso aberto
Palavra-chave:Nondifferentiable operator
Secant method
Descrição
Resumo:In this work we study a class of secant-like iterations for solving nonlinear equations in Banach spaces. We consider a condition for divided differences which generalizes the usual ones, i.e., Lipschitz and Hölder continuous conditions. A semilocal convergence result is obtained for nondifferentiable operators. For that, we use a technique based on a new system of recurrence relations to obtain domains of existence and uniqueness of the solution. Finally, we apply our results to the numerical solution of several examples. © 2002 Elsevier Science (USA). All rights reserved.