A family of third-order multipoint methods for solving nonlinear equations

We further present a new modification to the quadratically convergent iteration formulae proposed by Mamta et al. [Mamta, V. Kanwar, V.K. Kukreja, S. Singh, On a class of quadratically convergent iteration formulae, Appl. Math. Comput. 166 (2005) 633–637] for solving single variable nonlinear equations. It is proven that the modification converges cubically. Further, a new family with cubic convergence is obtained by discrete modification and the experiments show that the method is suitable in the cases where Steffensen or Newton–Steffensen methods fail. 2005 Elsevier Inc. All rights reserved.