On the local convergence of a family of two-step iterative methods for solving nonlinear equations

A local convergence analysis for a generalized family of two step Secant-like methods with frozen operator for solving nonlinear equations is presented. Unifying earlier methods such as Secant’s, Newton, Chebyshev-like, Steffensen and other new variants the family of iterative schemes is built up, w...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2014-01, Vol.255, p.753-764
Main Authors: Grau-Sánchez, Miquel, Noguera, Miquel, Diaz-Barrero, José L.
Format: Article
Language:English
Subjects:
Efficiency
Iterative methods
Nonlinear equations
Order of convergence
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Summary:A local convergence analysis for a generalized family of two step Secant-like methods with frozen operator for solving nonlinear equations is presented. Unifying earlier methods such as Secant’s, Newton, Chebyshev-like, Steffensen and other new variants the family of iterative schemes is built up, where a profound and clear study of the computational efficiency is also carried out. Numerical examples and an application using multiple precision and a stopping criterion are implemented without using any known root. Finally, a study comparing the order, efficiency and elapsed time of the methods suggested supports the theoretical results claimed.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2013.06.043