Geodesic
A continuous analogue of modified Newton method
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 2, pp. 67-71

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In the iterative Newton method we invert derivative of operator of equation for every step. In the modified Newton method we findinverse of derivative of operator only at initial point of iterative process. Then amount of calculations decreases and convergence speed falls. Continuous analog of Newton method is known. We construct the continuous analog of the modified Newton method for equation with strongly monotone operator in this note. We obtain sufficient conditions of strong convergence in Hilbert space for propose method.
Keywords: Hilbert space, strictly monotone operator, Frechet derivative, continuous method, operator of contraction
Mots-clés : convergence. 
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     author = {I. P. Ryazantseva and Bubnova O.Y.},
     title = {A continuous analogue of modified {Newton} method},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {67--71},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2016_18_2_a8/}
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I. P. Ryazantseva; Bubnova O.Y. A continuous analogue of modified Newton method. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 2, pp. 67-71. http://geodesic.mathdoc.fr/item/SVMO_2016_18_2_a8/