Geodesic
On convergence of finite dimensional approximations of $L$-regularized solutions
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 4, pp. 395-403 
V. P. Tanana; A. A. Shtarkman. On convergence of finite dimensional approximations of $L$-regularized solutions. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 4, pp. 395-403. http://geodesic.mathdoc.fr/item/SJVM_2000_3_4_a9/
@article{SJVM_2000_3_4_a9,
     author = {V. P. Tanana and A. A. Shtarkman},
     title = {On convergence of finite dimensional approximations of $L$-regularized solutions},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {395--403},
     year = {2000},
     volume = {3},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2000_3_4_a9/}
}
TY  - JOUR
AU  - V. P. Tanana
AU  - A. A. Shtarkman
TI  - On convergence of finite dimensional approximations of $L$-regularized solutions
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2000
SP  - 395
EP  - 403
VL  - 3
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SJVM_2000_3_4_a9/
LA  - ru
ID  - SJVM_2000_3_4_a9
ER  - 
%0 Journal Article
%A V. P. Tanana
%A A. A. Shtarkman
%T On convergence of finite dimensional approximations of $L$-regularized solutions
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2000
%P 395-403
%V 3
%N 4
%U http://geodesic.mathdoc.fr/item/SJVM_2000_3_4_a9/
%G ru
%F SJVM_2000_3_4_a9

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

Necessary and sufficient conditions for convergence of finite dimensional approximations of $L$-regularized solutions are obtained.

[1] Tikhonov A. N., “O regulyarizatsii nekorrektno postavlennykh zadach”, Dokl. AN SSSR, 153:1 (1963), 49–52 | MR | Zbl

[2] Tanana V. P., Metody resheniya operatornykh uravnenii, Nauka, M., 1981 | MR

[3] Menikhes L. D., Tanana V. P., “A convergense for approximation in the regularization method and the Tikhonov regularization method of $n$-th order”, J. Inv. Ill-Posed Problems, 6:3 (1998), 241–262 | MR

[4] Vasin V. V., Ageev A. L., Nekorrektnye zadachi s apriornoi informatsiei, Nauka, Ekaterinburg, 1993 | MR

[5] Kato T., Perturbation theory for linear operators, Springer-Verlag, New-York, 1966 | MR