Geodesic
Geometrical sense of Newton metods
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 1 (2009), pp. 4-12

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New geometrical sense of Newton methods for solving the system of nonlinear equations (in infinite-measuring case — nonlinear operational equations) found by us, clarifies completely its inner mechanism. From the point of view of application it enables to explain empirically observed effects, to get a unified characterization of the method and its modification, to get a general theorem on the problem of local convergence and to get a quite clear vision of geometrical-dynamic nature of convergence problem on the whole (both local and global). The results obtained are demonstrated on the model example.
Keywords: Newton method, Riemannian geometry, calculus of approximations, differentials equations. 
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     title = {Geometrical sense of {Newton} metods},
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M. V. Pchelintsev; N. A. Skorkin. Geometrical sense of Newton metods. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 1 (2009), pp. 4-12. http://geodesic.mathdoc.fr/item/VYURM_2009_1_a0/