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Directional Chebyshev-type methods for solving equations

Authors: I. K. Argyros, M. A. Hernández, S. Hilout and N. Romero
Journal: Math. Comp. 84 (2015), 815-830
MSC (2010): Primary 65H05, 65H10, 49M15
Published electronically: September 23, 2014
MathSciNet review: 3290965
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Abstract: A semi-local convergence analysis for directional Chebyshev-type methods in $ m$-variables is presented in this study. Our convergence analysis uses recurrent relations and Newton-Kantorovich-type hypotheses. Numerical examples are also provided to show the effectiveness of the proposed method.

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Additional Information

I. K. Argyros
Affiliation: Department of Mathematics and Sciences, Cameron University, Lawton, Oklahoma 73505

M. A. Hernández
Affiliation: Department of Mathematics and Computation, University of La Rioja, 26004 Logroño, Spain

S. Hilout
Affiliation: Laboratoire de Mathématiques et Applications and Département des Sciencesde la Terre et de l’Atmosphère Poitiers University, C.P. 8888 – Succursale Centreville Montréal, Québec, Canada

N. Romero
Affiliation: Department of Mathematics and Computation, University of La Rioja, 26004 Logroño, Spain

Keywords: Directional Chebyshev-type method, directional Newton--Secant method, nonlinear equations, Newton--Kantorovich hypotheses, recurrence relations, Hilbert space
Received by editor(s): September 6, 2011
Received by editor(s) in revised form: July 17, 2013
Published electronically: September 23, 2014
Additional Notes: The research of the second, third and fourth authors was supported in part by the project MTM2008-01952/MTM of the Spanish Ministry of Science and Innovation and the project Colabora 2009/04 of the Riojan Autonomous Community.
Article copyright: © Copyright 2014 American Mathematical Society

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