Geodesic
Continuous methods for stable approximation of solutions to nonlinear equations in the Banach space based on the regularized Newton--Kantarovich scheme
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 1, pp. 1-12.

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

We propose and study a class of methods for approximation of solutions to nonlinear equations with smooth operators in a Banach space, when the operators are approximately given and their derivatives are not regular. The construction of the presented methods is connected with the operator differential equation obtained by linearization of the original equation using the Newton–Kantorovich scheme and various ways of its regularization. When the initial discrepancy possesses a sourcewise representation, we establish estimates for the approximation errors. 
@article{SJVM_2004_7_1_a0,
     author = {A. B. Bakushinskii and M. Yu. Kokurin},
     title = {Continuous methods for stable approximation of solutions to nonlinear equations in the {Banach} space based on the regularized {Newton--Kantarovich} scheme},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {1--12},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2004_7_1_a0/}
}
TY  - JOUR
AU  - A. B. Bakushinskii
AU  - M. Yu. Kokurin
TI  - Continuous methods for stable approximation of solutions to nonlinear equations in the Banach space based on the regularized Newton--Kantarovich scheme
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2004
SP  - 1
EP  - 12
VL  - 7
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2004_7_1_a0/
LA  - ru
ID  - SJVM_2004_7_1_a0
ER  - 
%0 Journal Article
%A A. B. Bakushinskii
%A M. Yu. Kokurin
%T Continuous methods for stable approximation of solutions to nonlinear equations in the Banach space based on the regularized Newton--Kantarovich scheme
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2004
%P 1-12
%V 7
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2004_7_1_a0/
%G ru
%F SJVM_2004_7_1_a0
A. B. Bakushinskii; M. Yu. Kokurin. Continuous methods for stable approximation of solutions to nonlinear equations in the Banach space based on the regularized Newton--Kantarovich scheme. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 1, pp. 1-12. http://geodesic.mathdoc.fr/item/SJVM_2004_7_1_a0/

[1] Vainberg M. M., Variatsionnyi metod i metod monotonnykh operatorov, Nauka, M., 1972 | MR | Zbl

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

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

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

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

[6] Riss F., Sekefalvi-Nad B., Lektsii po funktsionalnomu analizu, Mir, M., 1979 | MR

[7] Krein S. G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967 | MR

[8] Trenogii V. A., Funktsionalnyi analiz, Nauka, M., 1980 | MR

[9] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1961 | MR