Geodesic
Determining the multiplicity of a root of a nonlinear algebraic equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 7, pp. 1181-1186 
N. N. Kalitkin; I. P. Poshivaylo. Determining the multiplicity of a root of a nonlinear algebraic equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 7, pp. 1181-1186. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_7_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Newton's method is most frequently used to find the roots of a nonlinear algebraic equation. The convergence domain of Newton's method can be expanded by applying a generalization known as the continuous analogue of Newton's method. For the classical and generalized Newton methods, an effective root-finding technique is proposed that simultaneously determines root multiplicity. Roots of high multiplicity (up to 10) can be calculated with a small error. The technique is illustrated using numerical examples.

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