Geodesic
On the approximate construction of an implicit function
Sbornik. Mathematics, Tome 40 (1981) no. 3, pp. 429-433 
A. A. Fonarev. On the approximate construction of an implicit function. Sbornik. Mathematics, Tome 40 (1981) no. 3, pp. 429-433. http://geodesic.mathdoc.fr/item/SM_1981_40_3_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The author considers an iterative projection method of constructing an implicit function under conditions that are satisfied in the standard implicit function theorem. It is shown that the method is applicable for finding solutions of equations under conditions analogous to those of the Newton–Kantorovich method. Bibliography: 7 titles.

[1] L. V. Kantorovich, G. P. Akilov, Funktsionalnyi analiz, izd-vo “Nauka”, Moskva, 1977 | MR | Zbl

[2] V. A. Trenogii, “Priblizheniya na semeistvakh banakhovykh prostranstv i razreshimost lineinykh uravnenii”, DAN SSSR, 201:6 (1971), 1288–1291

[3] V. A. Trenogii, “Neyavnye operatory i zadachi s singulyarnymi vozmuscheniyami”, Vsesoyuznaya konf. po asimptotich. metodam v teorii sing.-vozmusch. uravnenii, Tezisy dokladov, chast I, izd-vo “Nauka” Kaz. SSR, Alma-Ata, 1979, 12–13

[4] M. A. Krasnoselskii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, V. Ya. Stetsenko, Priblizhennoe reshenie operatornykh uravnenii, izd-vo “Nauka”, Moskva, 1969 | MR

[5] Zh.-P. Oben, Priblizhennoe reshenie ellipticheskikh kraevykh zadach, izd-vo “Mir”, Moskva, 1977 | MR

[6] A. Kartan, Differentsialnoe ischislenie. Differentsialnye formy, izd-vo “Mir”, Moskva, 1971 | MR

[7] S. D. Balashova, “O skhodimosti odnogo proektsionno-iteratsionnogo metoda”, Vychisl. matem. i programmirovanie, Dnepropetrovsk, 1976, 11–14