Geodesic
Calculation of roots and there multiplicity for nonlinear equation
Matematičeskoe modelirovanie, Tome 22 (2010) no. 7, pp. 33-52

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Different methods for calculation of nonlinear equation roots were compared. There of seconds method occuerd the most effective for simple roots. The methods of bisections and golden section were effective for multiple roots, but the last iterations should be performed by the method of seconds with the Aitken extrapolation for accuracy improving. All this methods termit to establish a root multiplicity. 
@article{MM_2010_22_7_a2,
     author = {N. N. Kalitkin and L. V. Kuzmina},
     title = {Calculation of roots and there multiplicity for nonlinear equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {33--52},
     publisher = {mathdoc},
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     number = {7},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_7_a2/}
}
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N. N. Kalitkin; L. V. Kuzmina. Calculation of roots and there multiplicity for nonlinear equation. Matematičeskoe modelirovanie, Tome 22 (2010) no. 7, pp. 33-52. http://geodesic.mathdoc.fr/item/MM_2010_22_7_a2/