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A family of iterative methods that uses divided differences of first and second orders

Autor
Ezquerro, J.A.; Grau, M.; Hernández-Verón, M.A.; Noguera, M.
Tipus d'activitat
Article en revista
Revista
Numerical algorithms
Data de publicació
2015-11-01
Volum
70
Número
3
Pàgina inicial
571
Pàgina final
589
DOI
https://doi.org/10.1007/s11075-015-9962-0 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/80873 Obrir en finestra nova
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 th...
Citació
Ezquerro, J.A., Grau, M., Hernández-Verón, M.A., Noguera, M. A family of iterative methods that uses divided differences of first and second orders. "Numerical algorithms", 01 Novembre 2015, vol. 70, núm. 3, p. 571-589.
Paraules clau
Convergence, Divided difference, Efficiency, Iterative methods, Nonlinear equations, Order of convergence, Secant method, Solving systems

Participants

  • Ezquerro, José Antonio  (autor)
  • Grau Sanchez, Miguel  (autor)
  • Hernández Verón, Miguel Angel  (autor)
  • Noguera Batlle, Miguel  (autor)

Arxius