Geodesic
A numerical method for solving systems of nonlinear equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 11, pp. 1827-1834 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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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