Solving a special case of conservative problems by Secant-like methods

We study a class of Secant-like iterations for solving nonlinear equations in Banach spaces. A semilocal convergence result is obtained, where the first order divided difference of the nonlinear operator is Hölder continuous. For that, we use a technique based on a new system of recurrence relations...

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Bibliographic Details
Authors: Hernández, M.A. [0000-0001-5478-2958], Rubio, M.J. [0000-0002-8765-4060], Ezquerro, J.A. [0000-0001-8120-167X]
Format: article
Status:Published version
Publication Date:2005
Country:España
Institution:Universidad de La Rioja (UR)
Repository:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc69fab750603269e824d2
Online Access:https://investigacion.unirioja.es/documentos/5bbc69fab750603269e824d2
Access Level:Open access
Keyword:A priori error bounds
Boundary value problems
Convergence analysis
Recurrence relations
The Secant method
Description
Summary:We study a class of Secant-like iterations for solving nonlinear equations in Banach spaces. A semilocal convergence result is obtained, where the first order divided difference of the nonlinear operator is Hölder continuous. For that, we use a technique based on a new system of recurrence relations to obtain existence-uniqueness domains of the solution and a priori error bounds. These results are applied to solve a special case of conservative problems. © 2004 Elsevier Inc. All rights reserved.