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An improvement of the region of accessibility of Chebyshev's method from Newton's method


Authors: J. A. Ezquerro and M. A. Hernández
Journal: Math. Comp. 78 (2009), 1613-1627
MSC (2000): Primary 47H99, 65J15
Published electronically: January 12, 2009
MathSciNet review: 2501066
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Abstract: A simple modification of Chebyshev's method is presented, so that the region of accessibility is extended to the one of Newton's method.


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Additional Information

J. A. Ezquerro
Affiliation: University of La Rioja, Department of Mathematics and Computation, C/ Luis de Ulloa s/n, 26004 Logroño, Spain
Email: jezquer@unirioja.es

M. A. Hernández
Affiliation: University of La Rioja, Department of Mathematics and Computation, C/ Luis de Ulloa s/n, 26004 Logroño, Spain
Email: mahernan@unirioja.es

DOI: https://doi.org/10.1090/S0025-5718-09-02193-0
Keywords: Nonlinear equations in Banach spaces, Newtons's method, Chebyshev's method, semilocal convergence theorem, $R$-order of convergence, region of accessibility
Received by editor(s): November 20, 2007
Received by editor(s) in revised form: May 19, 2008
Published electronically: January 12, 2009
Additional Notes: Preparation of this paper was partly supported by the Ministry of Education and Science (MTM 2005-03091).
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.