Geodesic
Truncated multidimensional Newton’s method
Matematičeskoe modelirovanie, Tome 24 (2012) no. 1, pp. 103-108

Voir la notice de l'article provenant de la source Math-Net.Ru

Simple generalization of the Newton’s method for systems of nonlinear equations was considered. It allows reducing a number of iterations until convergence if initial approximation is selected far from the exact solution. The suggested approach was tested for the problem which appears on solving of non-linear heat-conduction equation with several implicit schemes.
Keywords: Newton's method, systems of nonlinear equations, implicit methods for systems of ODE. 
@article{MM_2012_24_1_a6,
     author = {I. P. Poshivaylo},
     title = {Truncated multidimensional {Newton{\textquoteright}s} method},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {103--108},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2012_24_1_a6/}
}
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I. P. Poshivaylo. Truncated multidimensional Newton’s method. Matematičeskoe modelirovanie, Tome 24 (2012) no. 1, pp. 103-108. http://geodesic.mathdoc.fr/item/MM_2012_24_1_a6/