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
Any de publicació: 2015
Volum: 70
Número: 3
Pàgines: 571-589
Tipus: Article
beta Ver similares en nube de resultadosAltres publicacions en: Numerical Algorithms
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Resum
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.