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.
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