On a family of Laguerre methods to find multiple roots of nonlinear equations
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There are several methods for solving a nonlinear algebraic equation having roots of a given multiplicity m. Here we compare a family of Laguerre methods of order three as well as two others of the same order and show that Euler-Cauchy's method is best. We discuss the conjugacy maps and the e ect of the extraneous roots on the basins of attraction.
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