A family of three-step eighth-order iterative methods for solving nonlinear equations

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.