Ortega, J.M. and Rheinboldt, W.G. (1970) Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York.

has been cited by the following article:

• TITLE: Steffensen-Type Method of Super Third-Order Convergence for Solving Nonlinear Equations

  AUTHORS: Zhongli Liu, Hong Zhang

  KEYWORDS: Newton’s Method, Steffensen’s Method, Derivative Free, Super-Cubic Convergence, Nonlinear Equation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.2 No.7, June 13, 2014

  ABSTRACT: In this paper, a one-step Steffensen-type method with super-cubic convergence for solving nonlinear equations is suggested. The convergence order 3.383 is proved theoretically and demonstrated numerically. This super-cubic convergence is obtained by self-accelerating second-order Steffensen’s method twice with memory, but without any new function evaluations. The proposed method is very efficient and convenient, since it is still a derivative-free two-point method. Its theoretical results and high computational efficiency is confirmed by Numerical examples.