Geodesic
On some method of regularization for monotone equations in Hilbert space
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 1, pp. 70-74

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We study equations with monotone operators in Hilbert space with perturbed data. We construct for this ill-posed problem implicit iterative regularized method using continuous analogue of Newton method. In comparison with classical operator regularized method we introduce supplementary terms in right-hand side of regularized equation. By using a priori information of desired solution we choose initial approximation in this iterative method. We obtain sufficient conditions of strong convergence for propose method.
Keywords: monotone operator, approximate data, iterative method, regularization
Mots-clés : convergence. 
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     author = {I. P. Ryazantseva},
     title = {On some method of regularization for monotone equations in {Hilbert} space},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {70--74},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2016_18_1_a7/}
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I. P. Ryazantseva. On some method of regularization for monotone equations in Hilbert space. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 1, pp. 70-74. http://geodesic.mathdoc.fr/item/SVMO_2016_18_1_a7/