Geodesic
New implementations of the 2-factor method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 933-946

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The so-called 2-factor method was designed for finding singular solutions to nonlinear equations. New ways of implementing this method are proposed. So far, the known variants of the method used a very laborious iteration. Its implementation requires that the singular value decomposition be calculated for the derivative of the equation at hand. The new economical implementation is based on the Gaussian elimination with pivoting. In addition, the potentials for the globalization of convergence of the method are examined. In total, the proposed tools convert the conceptual sketch of the 2-factor method into a truly practical algorithm. 
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     author = {A. F. Izmailov},
     title = {New implementations of the 2-factor method},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {933--946},
     publisher = {mathdoc},
     volume = {55},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a3/}
}
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A. F. Izmailov. New implementations of the 2-factor method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 933-946. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a3/