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A general family of third order method for finding multiple roots
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| Organization: | University Mohammed First |
| Department: | MATSI Laboratory, ESTO |
| Organization: | University Mohammed First |
| Department: | MATSI Laboratory, ESTO |
| Organization: | University Mohammed First |
| Department: | MATSI Laboratory, ESTO |
| Organization: | University of Loraine |
| Department: | LITA Laboratory |
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| Applied Mathematics and Computation |
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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.
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