Geodesic
The method of determining all real nonmultiple roots of systems of nonlinear equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1486-1493 
V. Yu. Semënov. The method of determining all real nonmultiple roots of systems of nonlinear equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1486-1493. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A method for determining all nonmultiple roots of the system of nonlinear equations in an $n$-dimensional parallelepiped is proposed. The main idea of the method is that the original set, in which the roots are sought, is divided into subsets where either the system of equations does not have solutions or its Jacobian matrix is nonsingular. A partition algorithm is presented and its convergence is proved. The application of the method is demonstrated using several examples.

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