Geodesic
About the computation of simple and multiple roots of nonlinear equation
Matematičeskoe modelirovanie, Tome 20 (2008) no. 7, pp. 57-64

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Classical and generalized Newton methods as applied to the calculation of simple and multiple roots of nonlinear equation were examined. Algorithms for determining root's order during calculation were developed for both mentioned methods, which also allow to accelerate convergence for multiple roots. These algorithms are able to calculate roots even of a big order with a high accuracy. Careful examination of the algorithm details was accomplished, which allowed to write more precise and reliable program than existing standard ones. 
@article{MM_2008_20_7_a5,
     author = {N. N. Kalitkin and I. P. Poshivaylo},
     title = {About the computation of simple and multiple roots of nonlinear equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {57--64},
     publisher = {mathdoc},
     volume = {20},
     number = {7},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_7_a5/}
}
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N. N. Kalitkin; I. P. Poshivaylo. About the computation of simple and multiple roots of nonlinear equation. Matematičeskoe modelirovanie, Tome 20 (2008) no. 7, pp. 57-64. http://geodesic.mathdoc.fr/item/MM_2008_20_7_a5/