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.
Kanwar, V. (2006). A family of third-order multipoint methods for solving nonlinear equations. Applied Mathematics and Computation, 176(2), 409–413. https://doi.org/10.1016/j.amc.2005.09.029