Geodesic
Increasing the interval of convergence for a generalized Newton's method of solving nonlinear equations
Numerical methods and programming, Tome 17 (2016) no. 1, pp. 7-12.

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An approach to the construction of an extended interval of convergence for a previously proposed generalization of Newton's method to solve nonlinear equations of one variable. This approach is based on the boundedness of a continuous function defined on a segment. It is proved that, for the search for the real roots of a real-valued polynomial with complex roots, the proposed approach provides iterations with nonlocal convergence. This result is generalized to the case transcendental equations.
Keywords: iterative processes, Newton's method, logarithmic derivative, continuous functions defined on a segment, higher order methods
Mots-clés : interval of convergence, transcendental equations. 
@article{VMP_2016_17_1_a1,
     author = {A. N. Gromov},
     title = {Increasing the interval of convergence for a generalized {Newton's} method of solving nonlinear equations},
     journal = {Numerical methods and programming},
     pages = {7--12},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2016_17_1_a1/}
}
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A. N. Gromov. Increasing the interval of convergence for a generalized Newton's method of solving nonlinear equations. Numerical methods and programming, Tome 17 (2016) no. 1, pp. 7-12. http://geodesic.mathdoc.fr/item/VMP_2016_17_1_a1/