A family of iterative methods that uses divided differences of first and second orders
- Ezquerro, J.A. 2
- Grau-Sánchez, M. 1
- Hernández-Verón, M.A. 2
- Noguera, M. 1
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1
Universitat Politècnica de Catalunya
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2
Universidad de La Rioja
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ISSN: 1017-1398
Year of publication: 2015
Volume: 70
Issue: 3
Pages: 571-589
Type: Article
More publications in: Numerical Algorithms
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Abstract
The family of fourth-order Steffensen-type methods proposed by Zheng et al. (Appl. Math. Comput. 217, 9592–9597 (2011)) is extended to solve systems of nonlinear equations. This extension uses multidimensional divided differences of first and second orders. For a certain computational efficiency index, two optimal methods are identified in the family. Semilocal convergence is shown for one of these optimal methods under mild conditions. Moreover, a numerical example is given to illustrate the theoretical results.