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Title

A general family of third order method for finding multiple roots
Authors

D. Sbibih
Organization: University Mohammed First
Department: MATSI Laboratory, ESTO
A. Serghini
Organization: University Mohammed First
Department: MATSI Laboratory, ESTO
A. Tijini
Organization: University Mohammed First
Department: MATSI Laboratory, ESTO
A. Zidna
Organization: University of Loraine
Department: LITA Laboratory
Journal / Anthology

Applied Mathematics and Computation
Year: 2014
Volume: 233
Page range: 338350
Description

In this paper, we describe a general family of iterative methods for approximating a multiple root z with multiplicity m of a complex defined function. Almost of the family of the methods existing in the literature that use two-function and one-derivative evaluations are a special choice of this general method. We give some conditions to have the third order of convergence and we discuss how to choose a small asymptotic error constant which may be affect the speed of the convergence. Using Mathematica with its high precision compatibility, we present some numerical examples to confirm the theoretical results.
Subject

*Applied Mathematics