On the Efficiency of a Family of Steffensen-Like Methods with Frozen Divided Differences
- Amat, S. 1
- Busquier, S. 1
- Grau-Sánchez, M. 2
- Hernández-Verón, M.A. 3
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1
Universidad Politécnica de Cartagena
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2
Universitat Politècnica de Catalunya
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3
Universidad de La Rioja
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ISSN: 1609-4840
Year of publication: 2017
Volume: 17
Issue: 2
Pages: 187-199
Type: Article
More publications in: Computational Methods in Applied Mathematics
Abstract
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. © 2017 by De Gruyter.