V. Torkashvand - Young Researchers and Elite Club, Shahr-e-Qods Branch, Islamic Azad University, Tehran, ‎Iran.
M. Kazemi - Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, ‎Iran‎.

The primary goal of this work is to introduce general family Steffensen-like methods with memory of the high efficiency indices.To achieve this target two parameters are introduced which are calculated with the help of Newton’s interpolatory polynomial.It is shown that the R-order convergence of the proposed methods has been increased from ۲;۴;۸,and ۲^n to ۳.۵,۷,۱۴;and ۳.۵*۲^n-۱,respectively without any extra evaluation.Computational results confirm the efficient and robust character of presented methods.

Nonlinear equations, With memory methods, Acceleration of convergence, Efficiency index