Title :
A family of three-step eighth-order iterative methods for solving nonlinear equations
Author_Institution :
Dept. of Math., Bohai Univ., Jinzhou, China
Abstract :
In this paper, we present a family of three-step eighth-order iterative methods for solving nonlinear equations by using suitable Taylor and divided difference approximations. Per iteration the new methods require three evaluations of the function and one evaluation of its first derivative and therefore have the efficiency index equal to 1.682. Notice that Bi et al.´s method in [5] is a special case of the new family of methods. Numerical comparisons are made with several other existing methods to show the performance of the presented methods.
Keywords :
Newton method; approximation theory; nonlinear equations; Newton method; Taylor approximation; divided difference approximation; nonlinear equation; three-step eighth-order iterative method; Approximation methods; Bismuth; Convergence; Indexes; Iterative methods; Nonlinear equations; Taylor series; Eighth-order convergence; King´s methods; Newton method; Nonlinear equations; Root-finding;
Conference_Titel :
Electronic and Mechanical Engineering and Information Technology (EMEIT), 2011 International Conference on
Conference_Location :
Harbin, Heilongjiang
Print_ISBN :
978-1-61284-087-1
DOI :
10.1109/EMEIT.2011.6023796
