On estimating the error of an approximate solution caused by the discretization of an integral equation of the first kind
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 263-270
Voir la notice de l'article provenant de la source Math-Net.Ru
A regularizing algorithm for the approximate solution of integral equations of the first kind is investigated. The algorithm involves a finite-dimensional approximation of the problem; more exactly, the integral equation is discretized in two variables. An error estimate of the algorithm is obtained with the use of the equivalence of the generalized discrepancy method and the generalized discrepancy principle.
Keywords:
regularization, error estimate, ill-posed problem.
@article{TIMM_2016_22_1_a25,
author = {V. P. Tanana and A. I. Sidikova},
title = {On estimating the error of an approximate solution caused by the discretization of an integral equation of the first kind},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {263--270},
publisher = {mathdoc},
volume = {22},
number = {1},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a25/}
}
TY - JOUR AU - V. P. Tanana AU - A. I. Sidikova TI - On estimating the error of an approximate solution caused by the discretization of an integral equation of the first kind JO - Trudy Instituta matematiki i mehaniki PY - 2016 SP - 263 EP - 270 VL - 22 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a25/ LA - ru ID - TIMM_2016_22_1_a25 ER -
%0 Journal Article %A V. P. Tanana %A A. I. Sidikova %T On estimating the error of an approximate solution caused by the discretization of an integral equation of the first kind %J Trudy Instituta matematiki i mehaniki %D 2016 %P 263-270 %V 22 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a25/ %G ru %F TIMM_2016_22_1_a25
V. P. Tanana; A. I. Sidikova. On estimating the error of an approximate solution caused by the discretization of an integral equation of the first kind. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 263-270. http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a25/