On accuracy of Tikhonov regularization method of zeroth order at some classes of correctness
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 1 (2009), pp. 13-20 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article presents the research of accuracy of Tikhonov regularization method of zeroth order. The optimality according to the method at some classes of correctness is proved.
Keywords: solution method of operator equations, regularization method, module of continuity, error of method.
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N. M. Yaparova. On accuracy of Tikhonov regularization method of zeroth order at some classes of correctness. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 1 (2009), pp. 13-20. http://geodesic.mathdoc.fr/item/VYURM_2009_1_a1/

[1] A. I. Tikhonov, “O regulyarizatsii nekorrektno postavlennykh zadach”, Dokl. AN SSSR, 153:1 (1963), 49–52 | MR | Zbl

[2] I. M. Lifshits, “Ob opredelenii energeticheskogo spektra Boze-sistemy po ee teploemkosti”, ZhETF, 26:5 (1954), 551–556 | Zbl

[3] V. A. Korshunov, V. P. Tanana, “Opredelenie plotnosti sostoyanii po termodinamicheskim funktsiyam”, FMM, 48:5 (1979), 908–915

[4] V. K. Ivanov, “O lineinykh nekorrektnykh zadachakh”, Dokl. AN SSSR, 145:2 (1962), 270–272 | MR | Zbl

[5] V. K. Ivanov, V. V. Vasin, V. P. Tanana, Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya, Nauka, M., 1978, 208 pp. | MR

[6] V. K. Ivanov, T. I. Korolyuk, “Ob otsenke pogreshnosti pri reshenii nekorrektnykh zadach”, Zhurn. vychisl. matem. i matem. fiz., 9:1 (1969), 30–41 | MR | Zbl

[7] V. A. Morozov, S. F. Gilyazov, Optimalnaya regulyarizatsiya nekorrektnykh normalno razreshimykh operatornykh uravnenii, Izd-vo MGU, M., 1982, 270 pp.

[8] V. P. Tanana, M. A. Rekant, S. I. Yanchenko, Optimizatsiya metodov resheniya operatornykh uravnenii, Uralsk. un-t, Sverdlovsk, 1987, 200 pp. | MR | Zbl

[9] V. P. Tanana, Metody resheniya operatornykh uravnenii, Nauka, M., 1981, 180 pp. | MR

[10] U. Rudin, Funktsionalnyi analiz, Mir, M., 1975, 448 pp. | MR