Geodesic
Necessary conditions for a given convergence rate of iterative methods for solution of linear ill-posed operator equations in a~Banach space
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 4, pp. 295-310.

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

We study the rate of convergence of iterative methods for solution of linear ill-posed equations with sectorial operators in the Banach space. It is stated that the power sourcewise representation condition on the initial discrepancy with an arbitrary positive exponent which is sufficient for the power estimate of the convergence rate with the same exponent is actually close to be necessary and thus cannot be essentially relaxed. 
@article{SJVM_2002_5_4_a0,
     author = {M. Yu. Kokurin and V. V. Klyuchev},
     title = {Necessary conditions for a given convergence rate of iterative methods for solution of linear ill-posed operator equations in {a~Banach} space},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {295--310},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2002_5_4_a0/}
}
TY  - JOUR
AU  - M. Yu. Kokurin
AU  - V. V. Klyuchev
TI  - Necessary conditions for a given convergence rate of iterative methods for solution of linear ill-posed operator equations in a~Banach space
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2002
SP  - 295
EP  - 310
VL  - 5
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2002_5_4_a0/
LA  - ru
ID  - SJVM_2002_5_4_a0
ER  - 
%0 Journal Article
%A M. Yu. Kokurin
%A V. V. Klyuchev
%T Necessary conditions for a given convergence rate of iterative methods for solution of linear ill-posed operator equations in a~Banach space
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2002
%P 295-310
%V 5
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2002_5_4_a0/
%G ru
%F SJVM_2002_5_4_a0
M. Yu. Kokurin; V. V. Klyuchev. Necessary conditions for a given convergence rate of iterative methods for solution of linear ill-posed operator equations in a~Banach space. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 4, pp. 295-310. http://geodesic.mathdoc.fr/item/SJVM_2002_5_4_a0/

[1] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979 | MR

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

[3] Bakushinskii A. B., “K probleme postroeniya lineinykh regulyarizuyuschikh algoritmov v banakhovom prostranstve”, Zhurn. vychisl. matem. i mat. fiziki, 13:1 (1973), 204–210 | Zbl

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

[5] Plato R., Hamarik U., “On pseudo-optimal parameter choices and stopping rules for regularization methods in Banach spaces”, Numerical Functional Analysis and Optimization, 17:1–2 (1996), 181–195 | MR | Zbl

[6] Bakushinskii A. B., Kokurin M. Yu., “Usloviya istokopredstavimosti i skorost skhodimosti metodov resheniya nekorrektnykh operatornykh uravnenii. Ch. I”, Vychislitelnye metody i programmirovanie, Sb. nauch. tr., Izd-vo MGU, M., 2000, 64–84

[7] Kokurin M. Yu., “Uslovie istokopredstavimosti i otsenki skorosti skhodimosti metodov regulyarizatsii lineinykh uravnenii v banakhovom prostranstve. I”, Izvestiya vuzov. Matematika, 2001, no. 8, 51–59 | MR | Zbl

[8] Kokurin M. Yu., Operatornaya regulyarizatsiya i issledovanie nelineinykh monotonnykh zadach, Izd-vo MarGU, Ioshkar-Ola, 1998

[9] Engl H. W., Hanke M., Neubauer A., Regularization of Inverse Problems, Kluwer, Dordrecht, 1996 | MR | Zbl

[10] Kokurin M. Yu., Yusupova N. A., “O neobkhodimykh usloviyakh kvalifitsirovannoi skhodimosti metodov resheniya lineinykh nekorrektnykh zadach”, Izvestiya vuzov. Matematika, 2001, no. 2, 39–47 | MR | Zbl

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

[12] Krein S. G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967 | MR

[13] Kokurin M. Yu., Klyuchev V. V., “O neobkhodimom uslovii skhodimosti yavnogo iteratsionnogo protsessa dlya lineinykh uravnenii v banakhovom prostranstve”, Tezisy dokladov konferentsii “Obratnye i nekorrektno postavlennye zadachi”, MAKS Press, M., 2001, 39 | MR

[14] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, T. 2, Nauka, M., 1969

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

[16] Burbaki N., Integrirovanie (mera, integrirovanie mer), Nauka, M., 1967 | MR