%0 Journal Article
%T A family of optimal iterative methods with fifth and tenth order convergence for solving nonlinear equations
%A Mashallah Matinfar
%A Mohammad Aminzadeh
%J Journal of Interpolation and Approximation in Scientific Computing
%D 2012
%I International Scientific Publications and Consulting Services (ISPACS)
%R 10.5899/2012/jiasc-00012
%X In this paper, we propose a two-step method with fifth-order convergence and a family of optimal three-step method with tenth-order convergence for finding the simple roots of nonlinear equations. The optimal efficiency indices are all found to be $5^{frac{1}{3}}approx1.71$ and $10^{frac{1}{4}}approx1.78.$ Some numerical examples illustrate that the algorithms are more efficient and performs better than other methods.
%K Nonlinear equation
%K Iterative method
%K Three-step
%K Convergence order
%K Efficiency index
%U http://www.ispacs.com/journals/jiasc/2012/jiasc-00012/article.pdf