Improving the Dynamics of Steffensen-type Methods

Authors

Sergio Amat, Departamento de Matem´atica Aplicada y Estad´ıstica. Universidad Polit´ecnica de Cartagena, Spain.Follow
Sonia Busquier, Departamento de Matem´atica Aplicada y Estad´ıstica. Universidad Polit´ecnica de Cartagena, Spain.Follow
?ngel Alberto, Departamento de TFG/TFM, Universidad Internacional de La Rioja (UNIR), Logro?no, La Rioja, SpainFollow

Author Country (or Countries)

Spain.

Abstract

The dynamics of Steffesen-type methods, using a graphical tool for showing the basins of attraction, is presented. The study includes as particular cases, Steffesen-type modifications of the Newton, the two-steps, the Chebyshev, the Halley and the super– Halley iterative methods. The goal is to show that if we are interesting to preserve the convergence properties we must ensure that the derivatives are well approximated in all iterations.

Recommended Citation

Amat, Sergio; Busquier, Sonia; and Alberto, ?ngel (2023) "Improving the Dynamics of Steffensen-type Methods," Applied Mathematics & Information Sciences: Vol. 09: Iss. 5, Article 23.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss5/23