An efficient Steffensen-like iterative method with memory

作者：Cordero Alicia^*; Lotfi Taher; Khoshandi Arezoo; Torregrosa Juan R

来源：Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, 2015, 58(1): 49-58.

• Iterative methods
• R-order
• Steffensen-like methods with memory
• computational efficiency
• Herzberger's matrix
• stability
• basin of attraction

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.

• 出版日期2015