Improving the dynamics of steffensen-type methods

© 2015 NSP Natural Sciences Publishing Cor. 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.