%0 Journal Article
%T Steffensen-Type Method of Super Third-Order Convergence for Solving Nonlinear Equations
%A Zhongli Liu
%A Hong Zhang
%J Journal of Applied Mathematics and Physics
%P 581-586
%@ 2327-4379
%D 2014
%I Scientific Research Publishing
%R 10.4236/jamp.2014.27064
%X <p style=\"text-align:justify;\">
	<span style=\"font-size:12px;font-family:Verdana;\">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.</span> 
</p>
%K Newton¡¯s Method
%K Steffensen¡¯s Method
%K Derivative Free
%K Super-Cubic Convergence
%K Nonlinear Equation
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=46815