On the convergence of a class of generalized steffensen's iterative procedures and error analysis

Abstract

We consider a class of generalized Steffensen's methods for solving nonlinear equations without any derivative. We establish successful the existence-convergence theorem of generalized Steffensen's iteration under the Kantorovich-Ostrowski's conditions and present an upper bound, but it is not optimal. These conclusions contain the special case of Steffensen's method [6]. In the mean time, we compare the accurate error bound of Newton's method with error bounds of generalized Steffensen's methods, we show that latter is less than former.

Keywords:

• Nonlinear equations
• Traub-Kung two-point iterations
• Kantorovich theorem
• error analysis