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A multidimensional generalization of some classes of free-derivative iterative methods to solve nonlinear equations

Autor
Grau-Sanchez, M.; Noguera, M.
Tipus d'activitat
Article en revista
Revista
SeMA Journal: boletín de la Sociedad Española de Matemática Aplicada
Data de publicació
2017-12
Volum
74
Número
4
Pàgina inicial
543
Pàgina final
557
DOI
https://doi.org/10.1007/s40324-016-0100-2 Obrir en finestra nova
Resum
In this paper we extend to the multidimensional case six free-derivative iterative methods that are known in their scalar version. In order to construct new multidimensional iterative algorithms we develop a new idea based on two operators. All the schemes considered here are two-step methods in which the first step is Steffensen’s method and they have fourth-order local convergence, depending on the function. We analyze the efficiency of these six new algorithms and conclude which ones are th...
Paraules clau
Computational efficiency, Divided difference operators, Efficiency index, Iterative methods, Nonlinear equations, Order of convergence

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