Geodesic
Regular smoothness and the Newton–Kantorovich method
Trudy Instituta matematiki, Tome 19 (2011) no. 1, pp. 52-61 
P. P. Zabreiko; A. N. Tanyhina. Regular smoothness and the Newton–Kantorovich method. Trudy Instituta matematiki, Tome 19 (2011) no. 1, pp. 52-61. http://geodesic.mathdoc.fr/item/TIMB_2011_19_1_a5/
@article{TIMB_2011_19_1_a5,
     author = {P. P. Zabreiko and A. N. Tanyhina},
     title = {Regular smoothness and the {Newton{\textendash}Kantorovich} method},
     journal = {Trudy Instituta matematiki},
     pages = {52--61},
     year = {2011},
     volume = {19},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2011_19_1_a5/}
}
TY  - JOUR
AU  - P. P. Zabreiko
AU  - A. N. Tanyhina
TI  - Regular smoothness and the Newton–Kantorovich method
JO  - Trudy Instituta matematiki
PY  - 2011
SP  - 52
EP  - 61
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMB_2011_19_1_a5/
LA  - ru
ID  - TIMB_2011_19_1_a5
ER  - 
%0 Journal Article
%A P. P. Zabreiko
%A A. N. Tanyhina
%T Regular smoothness and the Newton–Kantorovich method
%J Trudy Instituta matematiki
%D 2011
%P 52-61
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/TIMB_2011_19_1_a5/
%G ru
%F TIMB_2011_19_1_a5

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

The article deals with the Newton–Kantorovich method for solving nonlinear operator equations under the regular smoothness assumption. The main convergence theorem is proved by means of the majorant method of Kantorovich.

[1] Galperin A., Waksman Z., “Newton's method under a weak smoothness assumption”, J. Comp. Appl. Math., 35 (1991), 207–215 | DOI | MR | Zbl

[2] Galperin A., Waksman Z., “Regular smoothness and Newton's method”, Numer. Funct. Anal. and Optimiz., 15:78 (1994), 813–858 | DOI | MR | Zbl

[3] Zabrejko P.P., Nguen D.F., “The majorant method in the theory of Newton–Kantorovich approximations and the Pták error estimates”, Numer. Funct. Anal. and Optimiz., 9:56 (1987), 671–684 | DOI | MR | Zbl