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Zbl 1198.65096
Ezquerro, J.A.; Hernández, M.A.
An improvement of the region of accessibility of Chebyshev's method from Newton's method. (English)
[J] Math. Comput. 78, No. 267, 1613-1627 (2009). ISSN 0025-5718; ISSN 1088-6842/e

Summary: A simple modification of Chebyshev's method is presented, so that the region of accessibility is extended to the one of Newton's method.
MSC 2000:
*65J15 Equations with nonlinear operators (numerical methods)
47H99 Nonlinear operators

Keywords: nonlinear equations in Banach spaces; Newtons's method; Chebyshev's method; semilocal convergence theorem; $R$-order of convergence; region of accessibility

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