Geodesic
Can an a priori error estimate for an approximate solution of an ill-posed problem be comparable with the error in data?
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 4, pp. 562-568
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For a linear operator equation of the first kind with perturbed data, it is shown that the global (on typical sets) a priori error estimate for its approximate solution can have the same order as that for the approximate data only if the operator of the problem is normally solvable. If the operator of the problem is given exactly, this is possible only if the problem is well-posed (stable). 
@article{ZVMMF_2014_54_4_a1,
     author = {A. S. Leonov},
     title = {Can an a priori error estimate for an approximate solution of an ill-posed problem be comparable with the error in data?},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {562--568},
     year = {2014},
     volume = {54},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_4_a1/}
}
TY  - JOUR
AU  - A. S. Leonov
TI  - Can an a priori error estimate for an approximate solution of an ill-posed problem be comparable with the error in data?
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2014
SP  - 562
EP  - 568
VL  - 54
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_4_a1/
LA  - ru
ID  - ZVMMF_2014_54_4_a1
ER  - 
%0 Journal Article
%A A. S. Leonov
%T Can an a priori error estimate for an approximate solution of an ill-posed problem be comparable with the error in data?
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2014
%P 562-568
%V 54
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_4_a1/
%G ru
%F ZVMMF_2014_54_4_a1
A. S. Leonov. Can an a priori error estimate for an approximate solution of an ill-posed problem be comparable with the error in data?. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 4, pp. 562-568. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_4_a1/

[1] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979 | MR

[2] Vainikko G. M., Veretennikov A. Yu., Iteratsionnye protsedury v nekorrektnykh zadachakh, Nauka, M., 1986 | MR

[3] Bakushinskii A. B., Goncharskii A. V., Iterativnye metody resheniya nekorrektnykh zadach, Nauka, M., 1989 | MR

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

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

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

[7] Tanana V. P., Rekant M. A., Yanchenko S. I., Optimizatsiya metodov resheniya operatornykh uravnenii, Izd-vo Uralskogo un-ta, Sverdlovsk, 1987 | MR

[8] Engl H. W., Hanke M., Neubauer A., Regularization of inverse problems, Kluwer Academic Publ., Dordrecht, 1996 | MR

[9] Bakushinskii A. B., Kokurin M. Yu., Iteratsionnye metody resheniya nekorrektnykh operatornykh uravnenii s gladkimi operatorami, Editorial URSS, M., 2002

[10] Bakushinsky A. B., Kokurin M. Yu., Iterative methods for approximate solution of inverse problems, Srpinger, Dordrecht, 2004, 292 pp. | MR

[11] Vinokurov V. A., “O pogreshnosti priblizhennogo resheniya lineinykh obratnykh zadach”, Dokl. AN SSSR, 246:4 (1979), 792–793 | MR

[12] Morozov V. A., Regulyarnye metody resheniya nekorrektno postavlennykh zadach, Nauka, M., 1987 | MR

[13] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965 | MR

[14] Tikhonov A. N., Leonov A. S., Yagola A. G., Nelineinye nekorrektnye zadachi, Nauka, M., 1995 | MR

[15] Edvards R., Funktsionalnyi analiz. Teoriya i prilozheniya, Mir, M., 1969

[16] Leonov A. S., Reshenie nekorrektno postavlennykh obratnykh zadach. Ocherk teorii, prakticheskie algoritmy i demonstratsii v MATLAB, URSS, M., 2010