Iteratively regularized methods for irregular nonlinear operator equations with a normally solvable derivative at the solution
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1543-1555
Voir la notice de l'article provenant de la source Math-Net.Ru
A group of iteratively regularized methods of Gauss–Newton type for solving irregular nonlinear equations with smooth operators in a Hilbert space under the condition of normal solvability of the derivative of the operator at the solution is considered. A priori and a posteriori methods for termination of iterations are studied, and estimates of the accuracy of approximations obtained are found. It is shown that, in the case of a priori termination, the accuracy of the approximation is proportional to the error in the input data. Under certain additional conditions, the same estimate is established for a posterior termination from the residual principle. These results generalize known similar estimates for linear equations with a normally solvable operator.
@article{ZVMMF_2016_56_9_a0,
author = {M. Yu. Kokurin},
title = {Iteratively regularized methods for irregular nonlinear operator equations with a normally solvable derivative at the solution},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1543--1555},
publisher = {mathdoc},
volume = {56},
number = {9},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a0/}
}
TY - JOUR AU - M. Yu. Kokurin TI - Iteratively regularized methods for irregular nonlinear operator equations with a normally solvable derivative at the solution JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2016 SP - 1543 EP - 1555 VL - 56 IS - 9 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a0/ LA - ru ID - ZVMMF_2016_56_9_a0 ER -
%0 Journal Article %A M. Yu. Kokurin %T Iteratively regularized methods for irregular nonlinear operator equations with a normally solvable derivative at the solution %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2016 %P 1543-1555 %V 56 %N 9 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a0/ %G ru %F ZVMMF_2016_56_9_a0
M. Yu. Kokurin. Iteratively regularized methods for irregular nonlinear operator equations with a normally solvable derivative at the solution. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1543-1555. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a0/