Geodesic
A numerical method for solving systems of nonlinear equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 11, pp. 1827-1834 
A. A. Abramov; L. F. Yukhno. A numerical method for solving systems of nonlinear equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 11, pp. 1827-1834. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_11_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Under certain conditions on nonlinear equations in a real finite-dimensional space, a numerical method for solving such equations is proposed. The method is based on the use of an auxiliary differential equation. A fairly rough approximate solution to this equation can be refined by applying Newton's method to the original problem. The result produced by the auxiliary equation is automatically a good initial approximation for Newton’s method. This combination ensures that the original problem can be solved to the required accuracy starting from any initial approximation.

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[4] Abramov A. A., Yukhno L. F., “Chislennoe reshenie zadachi Koshi dlya uravnenii Penleve. I; II”, Zh. vychisl. matem. i matem. fiz., 52:3 (2012), 379–387 | MR | Zbl