Geodesic
The Gauss–Newton method for finding singular solutions to systems of nonlinear equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 5, pp. 784-795

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An approach to the computation of singular solutions to systems of nonlinear equations is proposed. It consists in the construction of an (overdetermined) defining system to which the Gauss–Newton method is applied. This approach leads to completely implementable local algorithms without nondeterministic elements. Under fairly weak conditions, these algorithms have locally superlinear convergence. 
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     title = {The {Gauss{\textendash}Newton} method for finding singular solutions to systems of nonlinear equations},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_5_a2/}
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M. Yu. Erina; A. F. Izmailov. The Gauss–Newton method for finding singular solutions to systems of nonlinear equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 5, pp. 784-795. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_5_a2/