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An improvement of the region of accessibility of Chebyshev's method from Newton's method
Author(s):
J.
A.
Ezquerro;
M.
A.
Hernández.
Journal:
Math. Comp.
78
(2009),
1613-1627.
MSC (2000):
Primary 47H99, 65J15
Posted:
January 12, 2009
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Additional information
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.
References:
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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:
10.1090/S0025-5718-09-02193-0
PII:
S 0025-5718(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
Posted:
January 12, 2009
Additional Notes:
Preparation of this paper was partly supported by the Ministry of Education and Science (MTM 2005-03091).
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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