An efficient Steffensen-like iterative method with memory

[EN] Some methods with memory for solving nonlinear equations are designed from known methods without memory. We increase the convergence order from 4 to 6 by using a free parameter accelerator by Newton's interpolatory polynomial of the third degree. So, its efficiency index is even better than optimal sixteenth-order methods without memory. Dynamical behavior on low-degree polynomials is analyzed, highly improving the stability properties of the original schemes. Numerical test problems are given to prove its competitiveness with methods of the same class.
This research was supported by Ministerio de Ciencia y Tecnolog´ıa of Spain MTM2011-28636-C02-02. The second and third authors would like to appreciate Hamedan Branch of Islamic Azad University for their financial support. Moreover, we express our sincere thanks to the respected referees for their constructive suggestions and comments.