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A NOTE ON THE SEMILOCAL CONVERGENCE OF CHEBYSHEV’S METHOD

Part of: Numerical analysis in abstract spaces

Published online by Cambridge University Press:  15 October 2012

MANUEL A. DILONÉ ,
MARTÍN GARCÍA-OLIVO  and
JOSÉ M. GUTIÉRREZ
MANUEL A. DILONÉ*
Affiliation:
Dpto. de Investigación del ISFODOSU, Santo Domingo, Dominican Republic (email: dilonespinal@hotmail.es)
MARTÍN GARCÍA-OLIVO
Affiliation:
Politécnico Militar San Miguel Arcángel, Santo Domingo, Dominican Republic (email: martin1matdr@hotmail.com)
JOSÉ M. GUTIÉRREZ
Affiliation:
Dpto. de Matemáticas y Computación, Universidad de La Rioja, Logroño, Spain (email: jmguti@unirioja.es)
*
✉For correspondence; e-mail: dilonespinal@hotmail.es
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Abstract

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In this paper we develop a Kantorovich-like theory for Chebyshev’s method, a well-known iterative method for solving nonlinear equations in Banach spaces. We improve the results obtained previously by considering Chebyshev’s method as an element of a family of iterative processes.

Keywords

nonlinear equationsiterative methodsChebyshev’s methodKantorovich theory

MSC classification

Secondary: 65J15: Equations with nonlinear operators (do not use )
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 1 , August 2013 , pp. 98 - 105
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc. 

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