Geodesic
On Kaczmarz's iterative method and its generalizations
Sibirskij žurnal industrialʹnoj matematiki, Tome 9 (2006) no. 3, pp. 39-49.

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

@article{SJIM_2006_9_3_a4,
     author = {V. P. Il'in},
     title = {On {Kaczmarz's} iterative method and its generalizations},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {39--49},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2006_9_3_a4/}
}
TY  - JOUR
AU  - V. P. Il'in
TI  - On Kaczmarz's iterative method and its generalizations
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2006
SP  - 39
EP  - 49
VL  - 9
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2006_9_3_a4/
LA  - ru
ID  - SJIM_2006_9_3_a4
ER  - 
%0 Journal Article
%A V. P. Il'in
%T On Kaczmarz's iterative method and its generalizations
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2006
%P 39-49
%V 9
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2006_9_3_a4/
%G ru
%F SJIM_2006_9_3_a4
V. P. Il'in. On Kaczmarz's iterative method and its generalizations. Sibirskij žurnal industrialʹnoj matematiki, Tome 9 (2006) no. 3, pp. 39-49. http://geodesic.mathdoc.fr/item/SJIM_2006_9_3_a4/

[1] Kaczmarz S., “Angendherte Auflosung von Systemen Linearer Geichungen”, Bull. Internat. Acad. Polonaise Sci. Lett. Gl. Sci. Math., Nat. A, 1937, 355–357 | Zbl

[2] Kaczmarz S., “Approximate solution of systems of linear equations”, Internat. J. Control., 57:6 (1993), 1269–1271 | DOI | MR | Zbl

[3] Sovremennaya matematika dlya inzhenerov, Izd-vo inostr. lit., M., 1959

[4] Krutikov V. N., Petrova T. V., “Relaksatsionnyi metod minimizatsii s rastyazheniem prostranstva v napravlenii subgradienta”, Ekonomika i mat. metody, 39:1 (2003), 106–119 | Zbl

[5] Avedyan E. D., Tsypkin Ya. Z., “Obobschennyi algoritm Kachmazha”, Avtomatika i telemekhanika, 1979, no. 1, 72–78

[6] Voevodin V. V., Lineinaya algebra, Nauka, M., 1974 | MR | Zbl

[7] Vazov V., Forsait Dzh., Raznostnye metody resheniya differentsialnykh uravnenii v chastnykh proizvodnykh, Izd-vo inostr. lit., M., 1963 | MR

[8] Tanabe K., “Projection method for solving a singular system of linear equation and its applications”, Numer. Math., 17 (1971), 203–214 | DOI | MR | Zbl

[9] Vasilchenko G. P., Svetlanov A. A., “Proektsionnyi algoritm resheniya sistem lineinykh algebraicheskikh uravnenii bolshoi razmernosti”, Zhurn. vychisl. matematiki i mat. fiziki, 20:1 (1980), 3–10 | MR

[10] Bramble J. H., Pasciak J. E., Wang J., Xu J., “Convergence estimates for product iterative methods with applications to domain decomposition”, Math. Comp., 57:195 (1991), 1–21 | DOI | MR | Zbl

[11] Hackbush W., Multigrid Methods and Applications, Springer-Verl., Berlin, 1985

[12] Ilin V. P., Metody konechnykh raznostei i konechnykh ob'emov dlya ellipticheskikh uravnenii, Izd-vo Instituta matematiki, Novosibirsk, 2000

[13] Saad J., Iterative Methods for Spars Linear Systems, EPS, Boston, 1996

[14] Andreeva M. Yu., Il'in V. P., Itskovich E. A., “Two solvers for nonsymmetric SLAE”, Bull. Novosibirsk Comp. Center. Numer. Anal., 12:12 (2004), 1–16

[15] Golub G., Van Loan C., Matrix Computations, John Hopkins Univ. Press, Baltimore, 1989 | MR | Zbl

[16] Appleby G., Smolarski D. C., “A linear acceleration row action method for projecting onto subspaces”, Electron. Trans. Numer. Anal., 20 (2005), 243–275 | MR