Geodesic
Iterative Newton-type methods with projecting for solution of nonlinear ill-posed operator equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 2, pp. 101-111.

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We propose and study a class of iterative methods of the Newton type for approximate solution of nonlinear ill-posed operator equations without the regularity property. A possible a priori information concerning the unknown solution is treated by the projecting onto a closed convex subset containing the solution. The two ways of arranging of the computational process are considered. The first one requires the stopping of iterations at an appropriate step, while the second ensures obtaining of an iterative sequence which stabilizes within a small neighborhood of the solution. 
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A. B. Bakushinskii; M. Yu. Kokurin; N. A. Yusupova. Iterative Newton-type methods with projecting for solution of nonlinear ill-posed operator equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 2, pp. 101-111. http://geodesic.mathdoc.fr/item/SJVM_2002_5_2_a1/

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

[2] Bakushinsky A., Goncharsky A., Ill-posed problems: Theory and applications, Kluwer, Dordrecht, 1996

[3] Lavrentev M. M., Romanov V. G., Shishatskii S. P., Nekorrektnye zadachi matematicheskoi fiziki i analiza, Nauka, M., 1980 | MR

[4] Bukhgeim A. L., Vvedenie v teoriyu obratnykh zadach, Nauka, Novosibirsk, 1988 | MR

[5] Tikhonov A. N., Goncharskii A. V., Stepanov V. V., Yagola A. G., Regulyarizuyuschie algoritmy i apriornaya informatsiya, Nauka, M., 1983 | MR

[6] Vasin V. V., Ageev A. L., Nekorrektnye zadachi s apriornoi informatsiei, UIF “Nauka”, Ekaterinburg, 1993 | MR

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

[8] Bakushinskii A. B., “Iteratsionnye metody bez nasyscheniya dlya resheniya vyrozhdennykh nelineinykh operatornykh uravnenii”, Dokl. RAN, 344:1 (1995), 7–8 | MR

[9] Bakushinskii A. B., “Iterativnye metody dlya resheniya nelineinykh operatornykh uravnenii bez svoistva regulyarnosti”, Fundamentalnaya i prikladnaya matematika, 3:3 (1997), 685–692 | MR

[10] Bakushinskii A. B., “O skorosti skhodimosti iteratsionnykh protsessov dlya nelineinykh operatornykh uravnenii”, Zhurn. vychisl. matem. i mat. fiziki, 38:4 (1998), 559–563 | MR | Zbl

[11] Kokurin M. Yu., Yusupova N. A., “O nevyrozhdennykh otsenkakh skorosti skhodimosti iteratsionnykh metodov resheniya nekorrektnykh nelineinykh operatornykh uravnenii”, Zhurn. vychisl. matem. i mat. fiziki, 40:6 (2000), 832–837 | MR | Zbl

[12] Bakushinskii A. B., Kokurin M. Yu., Yusupova N. A., “Neobkhodimye usloviya skhodimosti iteratsionnykh metodov resheniya nelineinykh operatornykh uravnenii bez svoistva regulyarnosti”, Zhurn. vychisl. matem. i mat. fiziki, 40:7 (2000), 986–996 | MR

[13] Bakushinskii A. B., “Iterativnye metody gradientnogo tipa dlya neregulyarnykh operatornykh uravnenii”, Zhurn. vychisl. matem. i mat. fiziki, 38:12 (1998), 1962–1966 | MR | Zbl

[14] Bakushinskii A. B., “Iterativnye metody gradientnogo tipa s proektirovaniem na fiksirovannoe podprostranstvo dlya resheniya neregulyarnykh operatornykh uravnenii”, Zhurn. vychisl. matem. i mat. fiziki, 40:10 (2000), 1447–1450 | MR

[15] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Nauka, M., 1981 | MR

[16] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1981 | MR

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