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

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

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. 
@article{SVMO_2016_18_1_a7,
     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/}
}
TY  - JOUR
AU  - I. P. Ryazantseva
TI  - On some method of regularization for monotone equations in Hilbert space
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2016
SP  - 70
EP  - 74
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2016_18_1_a7/
LA  - ru
ID  - SVMO_2016_18_1_a7
ER  - 
%0 Journal Article
%A I. P. Ryazantseva
%T On some method of regularization for monotone equations in Hilbert space
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2016
%P 70-74
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2016_18_1_a7/
%G ru
%F SVMO_2016_18_1_a7
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/

[1] Vainberg M.M., Variatsionnyi metod i metod monotonnykh operatorov v teorii nelineinykh uravnenii, Nauka, Moskva, 1972 | MR

[2] Alber Ya., Ryazantseva I., Nonlinear ill-posed problems of monotone type, Springer, Dordrecht, 2006 | MR | Zbl

[3] Gavurin M.K., “Nelineinye funktsionalnye uravneniya i nepreryvnye analogi iterativnykh metodov”, Izvestiya vuzov. Matematika, 1958, no. 5(6), 18–31 | MR | Zbl

[4] Trenogin V.A., Funktsionalnyi analiz, Nauka, Moskva, 1980 | MR

[5] Ryazantseva I.P., “O nekotorykh metodakh nepreryvnoi regulyarizatsii dlya monotonnykh uravnenii”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 34:1 (1994), 3–11 | MR | Zbl

[6] Ryazantseva I.P., Izbrannye glavy teorii operatorov monotonnogo tipa, NGTU, Nizhnii Novgorod, 2008

[7] Tikhonov A.N., Goncharskii A.V., Stepanov V.V., Yagola A.G., Regulyarizovannye algoritmy i apriornaya informatsiya, Nauka, Moskva, 1983 | MR

[8] Tikhonov A.N., Goncharskii A.V., Stepanov V.V., Yagola A.G., Chislennye metody resheniya nekorrektnykh zadach, Nauka, Moskva, 1990 | MR