@article{ZVMMF_2003_43_9_a1,
author = {V. S. Sizikov},
title = {Discrepancy methods for solving ill posed problems},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1294--1312},
year = {2003},
volume = {43},
number = {9},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_9_a1/}
}
V. S. Sizikov. Discrepancy methods for solving ill posed problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 9, pp. 1294-1312. http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_9_a1/
[1] Vinokurov V. A., “O pogreshnosti priblizhennogo resheniya lineinykh obratnykh zadach”, Dokl. AN SSSR, 246:4 (1979), 792–793 | MR | Zbl
[2] Leonov A. S., Yagola A. G., “Adaptivnye optimalnye algoritmy resheniya nekorrektnykh zadach s istokoobrazno predstavimymi resheniyami”, Zh. vychisl. matem. i matem. fiz., 41:6 (2001), 855–873 | MR | Zbl
[3] Ivanov V. K., Vasin V. V., Tanana V. P., Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya, Nauka, M., 1978 | MR
[4] Bakushinskii A. B., Goncharskii A. V., Iterativnye metody resheniya nekorrektnykh zadach, Nauka, M., 1989 | MR
[5] Tikhonov A. N., Leonov A. S., Yagola A. G., Nelineinye nekorrektnye zadachi, Nauka, M., 1995 | MR
[6] Vainikko G. M., Veretennikov A. Yu., Iteratsionnye protsedury v nekorrektnykh zadachakh, Nauka, M., 1986 | MR
[7] Kojdecki M. A., “New criterion of regularization parameter choice in Tikhonov's method”, Biuletyn WAT (Bulletin of Military University of Technology), 49:1 (569) (2000), 47–126
[8] Kojdecki M. A., “Examples of saturated convergence rates for Tikhonov regularization”, BIT, 41:5 (2001), 1059–1068 | DOI | MR
[9] Groetsch C. W., Scherzer O., “Optimal order of convergence for stable evaluation of differential operators”, Electron. J. Different. Equat., 1993, no. 04 | MR
[10] Gfrerer H., “An a posteriori parameter choice for ordinary and iterated Tikhonov regularization of ill-posed problems leading to optimal convergence rates”, Math. Comput., 49 (1987), 507–522 | DOI | MR | Zbl
[11] Engl H. W., Gfrerer H., “A posteriori parameter choice for general regularization methods for solving linear ill-posed problems”, Appl. Numer. Math., 4 (1988), 395–417 | DOI | MR | Zbl
[12] Tikhonov A. N., Goncharskii A. V., Stepanov V. V., Yagola A. G., Chislennye metody resheniya nekorrektnykh zadach, Nauka, M., 1990 | MR
[13] Morozov V. A., Regulyarnye metody resheniya nekorrektno postavlennykh zadach, Nauka, M., 1987 | MR
[14] Groetsch C. W., The theory of Tikhonov regularization for Fredholm equations of the first king, Pitman, Boston, 1984 | MR | Zbl
[15] Engl H. W., Hanke M., Neubauer A., Regularization of inverse problems, Kluwer, Dordrecht, 1996 | MR | Zbl
[16] Engl H. W., “Discrepancy principles for Tikhonov regularization of ill-posed problems leading to optimal convergence rates”, J. Optimizat. Theory Appl., 49 (1987), 209–215 | DOI | MR
[17] Groetsch C. W., Inverse problems in the mathematical sciences, AMS, Providence, 1993 | MR
[18] Verlan A. F., Sizikov B. C., Integralnye uravneniya: metody, algoritmy, programmy, Nauk. dumka, Kiev, 1986 | MR
[19] Sizikov B. C., “Analiz metodov lokalnoi regulyarizatsii i formulirovka metoda suboptimalnoi filtratsii resheniya uravnenii I roda”, Zh. vychisl. matem. i matem. fiz., 39:5 (1999), 718–733 | MR | Zbl
[20] Turchin V. F., “Vybor ansamblya gladkikh funktsii pri reshenii obratnoi zadachi”, Zh. vychisl. matem. i matem. fiz., 8:1 (1968), 230–238
[21] Engl H., Analyse und Numerik schlecht gestellter Probleme, J. Kepler Univ., Linz, 1980
[22] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Izd. 6-e, Nauka, M., 1989 | MR
[23] Shikin E. V., Plis A. I., Krivye i poverkhnosti na ekrane kompyutera. Rukovodstvo po splainam dlya polzovatelei, DIALOG-MIFI, M., 1996
[24] Sizikov B. C., Matematicheskie metody obrabotki rezultatov izmerenii, Politekhnika, SPb., 2001 | MR