In this paper we deal with iterative methods for approximating multiple roots of nonlinear equations, it is a special case where some particular aspects must be taken into account. We are interested in local convergence studies, that is in obtaining an open ball B(α, r) where the sequence x_n generated by an iterative method, starting from any initial point in it generates a sequence {x_n} that remains in the ball and converges to the solution of the problem, α. Then, it is interesting to obtain the largest possible value of r, but obviously, this depends on the conditions that the nonlinear function verifies. We define a new technique to simplify the process of obtaining the functions that bound the error equation just by using a characterization of the function using Taylor's development around the root under the assumption of a bounding condition for the (m + 1)th derivative of the function f (x). This technique simplifies the usual intricate properties of divided differences that are used in already published papers about local convergence for multiple roots. Moreover, we complete the study in cases where the multiplicity m is unknown, so we estimate this factor by different strategies comparing the behavior of the corresponding estimations and how this fact affect to the original method.
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