Regularization of operator equations with $B$-symmetric and $B$-positive operators in Banach spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2009), pp. 81-87.

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

In this paper we consider a family of regularization methods for linear operator equations with $B$-symmetric and $B$-positive operators. We establish convergence theorems for regularized solutions and their discrete approximations.
Keywords: $B$-symmetric operator, $B$-positive operator, uniformly convex space, Efimov–Stechkin space, discretization, iterative process, subgradient, subdifferential.
@article{IVM_2009_10_a10,
     author = {P. A. Chistyakov},
     title = {Regularization of operator equations with $B$-symmetric and $B$-positive operators in {Banach} spaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {81--87},
     publisher = {mathdoc},
     number = {10},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_10_a10/}
}
TY  - JOUR
AU  - P. A. Chistyakov
TI  - Regularization of operator equations with $B$-symmetric and $B$-positive operators in Banach spaces
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2009
SP  - 81
EP  - 87
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2009_10_a10/
LA  - ru
ID  - IVM_2009_10_a10
ER  - 
%0 Journal Article
%A P. A. Chistyakov
%T Regularization of operator equations with $B$-symmetric and $B$-positive operators in Banach spaces
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2009
%P 81-87
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2009_10_a10/
%G ru
%F IVM_2009_10_a10
P. A. Chistyakov. Regularization of operator equations with $B$-symmetric and $B$-positive operators in Banach spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2009), pp. 81-87. http://geodesic.mathdoc.fr/item/IVM_2009_10_a10/

[1] Tikhonov A. N., “O reshenii nekorrektno postavlennykh zadach i metode regulyarizatsii”, DAN SSSR, 151:3 (1963), 501–504 | MR | Zbl

[2] Tikhonov A. N., “O regulyarizatsii nekorrektno postavlennykh zadach”, DAN SSSR, 153:1 (1963), 48–52 | MR

[3] Lavrentev M. M., O nekotorykh nekorrektnykh zadachakh matematicheskoi fiziki, Izd-vo SO AN SSSR, Novosibirsk, 1962, 92 pp. | MR

[4] Ivanov V. K., Vasin V. V., Tanana V. P., Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya, Nauka, M., 1978, 206 pp. | MR

[5] Birman M. Sh., “O metode Fridrikhsa rasshireniya polozhitelno opredelennogo operatora do samosopryazhennogo”, Zap. Leningr. gornogo in-ta, 33:3 (1956), 132–136 | MR

[6] Shalov V. M., “Reshenie nesamosopryazhennykh uravnenii variatsionnym metodom”, DAN SSSR, 151:3 (1963), 511–512 | Zbl

[7] Kalyakin L. A., “O priblizhennom reshenii nekorrektnykh zadach v normirovannykh prostranstvakh”, Zhurn. vychisl. matem. i matem. fiziki, 12:5 (1972), 1168–1181

[8] Vainikko G. M., Analiz diskretizatsionnykh metodov, Izd-vo Tart. un-ta, Tartu, 1976, 161 pp. | MR

[9] Stummel F., “Diskrete Konvergenz linear Operatoren. I”, Math. Ann., 190:1 (1970), 45–92 | DOI | MR | Zbl

[10] Stummel F., “Diskrete Konvergenz linear Operatoren. II”, Math. Z., 120 (1971), 231–264 | DOI | MR | Zbl

[11] Vasin V. V., Ageev A. L., Nekorrektnye zadachi s apriornoi informatsiei, UIF “Nauka”, Ekaterinburg, 1993, 264 pp. | MR

[12] Demyanov V. F., Vasilev V. P., Nedifferentsiruemaya optimizatsiya, Nauka, M., 1981, 384 pp. | MR

[13] Polyak B. T., Vvedenie v optimizatsiyu, Nauka, M., 1983, 384 pp. | MR