Geodesic
Iterative methods of stochastic approximation for solving non-regular nonlinear operator equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 10, pp. 1637-1645

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

Iterative methods for solving non-regular nonlinear operator equations in a Hilbert space under random noise are constructed and examined. The methods use the averaging of the input data. It is not assumed that the noise dispersion is known. An iteratively regularized method of order zero for equations with monotone operators and iteratively regularized methods of the Gauss–Newton type for equations with arbitrary smooth operators are used as the basic procedures. It is shown that the generated approximations converge in the mean-square sense to the desired solution or stabilize (again in the mean-square sense) in a small neighborhood of the solution. 
@article{ZVMMF_2015_55_10_a1,
     author = {A. B. Bakushinskii and M. Yu. Kokurin},
     title = {Iterative methods of stochastic approximation for solving non-regular nonlinear operator equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1637--1645},
     publisher = {mathdoc},
     volume = {55},
     number = {10},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_10_a1/}
}
TY  - JOUR
AU  - A. B. Bakushinskii
AU  - M. Yu. Kokurin
TI  - Iterative methods of stochastic approximation for solving non-regular nonlinear operator equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 1637
EP  - 1645
VL  - 55
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_10_a1/
LA  - ru
ID  - ZVMMF_2015_55_10_a1
ER  - 
%0 Journal Article
%A A. B. Bakushinskii
%A M. Yu. Kokurin
%T Iterative methods of stochastic approximation for solving non-regular nonlinear operator equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 1637-1645
%V 55
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_10_a1/
%G ru
%F ZVMMF_2015_55_10_a1
A. B. Bakushinskii; M. Yu. Kokurin. Iterative methods of stochastic approximation for solving non-regular nonlinear operator equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 10, pp. 1637-1645. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_10_a1/