Second-Derivative-Free Variant of the Chebyshev Method for Nonlinear Equations

M. A. Hernández
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M. A. Hernández: University of La Rioja

Journal of Optimization Theory and Applications, 2000, vol. 104, issue 3, No 1, 515 pages

Abstract: Abstract In this paper, we introduce a numerical method for nonlinear equations, based on the Chebyshev third-order method, in which the second-derivative operator is replaced by a finite difference between first derivatives. We prove a semilocal convergence theorem which guarantees local convergence with R-order three under conditions similar to those of the Newton-Kantorovich theorem, assuming the Lipschitz continuity of the second derivative. In a subsequent theorem, the latter condition is replaced by the weaker assumption of Lipschitz continuity of the first derivative.

Keywords: Chebyshev method; nonlinear equations in Banach spaces; third-order methods; multipoint iterations (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1004618223538

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