| Abstract: | In this article we present a third-order family of methods for solving nonlinear equations. Some well-known methods belong to our family, for example Halley's method, method (24) from M. Basto, V. Semiao, and F.L. Calheiros, A new iterative method to compute nonlinear equations, Appl. Math. Comput. 173 (2006), pp. 468–483] and the super-Halley method from J.M. Gutierrez and M.A. Hernandez, An acceleration of Newton's method: Super-Halley method, Appl. Math. Comput. 117 (2001), pp. 223–239]. The convergence analysis shows the third order of our family. We also give sufficient conditions for the stopping inequality |x n+1?α|≤|x n+1?x n | for this family. Comparison of the family members shows that there are no significant differences between them. Several examples are presented and compared. |
