Geodesic
Constructing regularization methods in the spaces of differentiable functions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 11, pp. 1915-1922 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The method of finding approximations to a solution and its derivatives is constructed for a certain class of integral Volterra equations of the first kind. Matching conditions for the regularization parameter and the error in the initial data are presented. Sharp (in terms of order) error estimates are obtained for approximate solutions on certain compact classes. 
@article{ZVMMF_2006_46_11_a0,
     author = {G. V. Khromova and E. V. Shishkova},
     title = {Constructing regularization methods in the spaces of differentiable functions},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1915--1922},
     year = {2006},
     volume = {46},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a0/}
}
TY  - JOUR
AU  - G. V. Khromova
AU  - E. V. Shishkova
TI  - Constructing regularization methods in the spaces of differentiable functions
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 1915
EP  - 1922
VL  - 46
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a0/
LA  - ru
ID  - ZVMMF_2006_46_11_a0
ER  - 
%0 Journal Article
%A G. V. Khromova
%A E. V. Shishkova
%T Constructing regularization methods in the spaces of differentiable functions
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 1915-1922
%V 46
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a0/
%G ru
%F ZVMMF_2006_46_11_a0
G. V. Khromova; E. V. Shishkova. Constructing regularization methods in the spaces of differentiable functions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 11, pp. 1915-1922. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a0/

[1] Khromova G. V., “O differentsirovanii funktsii, zadannykh s pogreshnostyu”, Differents. ur-niya i vychisl. matem., 6, Izd-vo Saratovskogo un-ta, Saratov, 1984, 53–58

[2] Khromova G. V., “Ob otsenkakh pogreshnosti priblizhennykh reshenii uravnenii pervogo roda”, Dokl. RAN, 378:5 (2001), 605–609 | MR | Zbl

[3] Shishkova E. V., “Reshenie zadachi Kolmogorova–Nikolskogo dlya integralnykh operatorov s polinomialnymi finitnymi yadrami”, Matem. Mekhan., Sb. nauch. tr., 6, Izd-vo Saratovskogo un-ta, Saratov, 2004, 149–152

[4] Khromova G. V., “O regulyarizatsii odnogo klassa integralnykh uravnenii pervogo roda”, Zh. vychisl. matem. i matem. fiz., 45:10 (2005), 1810–1817 | MR | Zbl

[5] Khromova G. V., “Ob odnom sposobe postroeniya metodov regulyarizatsii uravnenii I roda”, Zh. vychisl. matem. i matem. fiz., 40:7 (2000), 997–1002 | MR

[6] Bakushinskii A. B., Goncharskii A. B., Nekorrektnye zadachi. Chislennye metody i prilozheniya, MGU, M., 1989

[7] Ivanov V. K., Bushmanova M. V., “Otsenki ustoichivosti pri reshenii operatornykh uravnenii pervogo roda metodom regulyarizatsii”, Izv. vuzov. Matematika, 1976, no. 1(164), 48–54 | Zbl

[8] Khromova G. V., “O metode regulyarizatsii Tikhonova dlya integralnogo uravneniya s razryvnym yadrom”, Obratnye i nekorrektno postavlennye zadachi, Tez. dokl. konferentsii, Izd-vo Mosk. un-ta, M., 1998, 87