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Computational Methods in Applied Mathematics

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Volume 17, Issue 2


On the Efficiency of a Family of Steffensen-Like Methods with Frozen Divided Differences

Sergio Amat
  • Corresponding author
  • Department of Applied Mathematics and Statistics, Technical University of Cartagena, 30203 Cartagena (Murcia), Spain
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  • De Gruyter OnlineGoogle Scholar
/ Sonia Busquier
  • Department of Applied Mathematics and Statistics, Technical University of Cartagena, 30203 Cartagena (Murcia), Spain
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  • Other articles by this author:
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/ Miquel Grau-Sánchez / Miguel A. Hernández-Verón
Published Online: 2016-12-21 | DOI: https://doi.org/10.1515/cmam-2016-0039


A generalized k-step iterative method from Steffensen’s method with frozen divided difference operator for solving a system of nonlinear equations is studied and the maximum computational efficiency is computed. Moreover, a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the method and the computational efficiency are both well deduced. By using a technique based on recurrence relations, the semilocal convergence of the family is studied. Finally, some numerical experiments related to the approximation of nonlinear elliptic equations are reported. A comparison with other derivative-free families of iterative methods is carried out.

Keywords: Nonlinear Equations; Iterative Methods; Frozen Divided Difference; Order of Convergence, Efficiency

MSC 2010: 65H10; 65Y20


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About the article

Received: 2016-07-20

Revised: 2016-11-09

Accepted: 2016-11-15

Published Online: 2016-12-21

Published in Print: 2017-04-01

This work was supported in part by the project MTM2011-28636-C02-01 of the Spanish Ministry of Science and Innovation. Research supported in part by Programa de Apoyo a la investigación de la fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 19374/PI/14 and MTM2015-64382-P (MINECO/FEDER).

Citation Information: Computational Methods in Applied Mathematics, Volume 17, Issue 2, Pages 187–199, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2016-0039.

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