Geodesic
On a solving ill-conditioned linear systems by iterative methods
Matematičeskoe modelirovanie, Tome 16 (2004) no. 7, pp. 13-20 
A. S. Pavlov; L. F. Yukhno. On a solving ill-conditioned linear systems by iterative methods. Matematičeskoe modelirovanie, Tome 16 (2004) no. 7, pp. 13-20. http://geodesic.mathdoc.fr/item/MM_2004_16_7_a2/
@article{MM_2004_16_7_a2,
     author = {A. S. Pavlov and L. F. Yukhno},
     title = {On a solving ill-conditioned linear systems by iterative methods},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {13--20},
     year = {2004},
     volume = {16},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_7_a2/}
}
TY  - JOUR
AU  - A. S. Pavlov
AU  - L. F. Yukhno
TI  - On a solving ill-conditioned linear systems by iterative methods
JO  - Matematičeskoe modelirovanie
PY  - 2004
SP  - 13
EP  - 20
VL  - 16
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/MM_2004_16_7_a2/
LA  - ru
ID  - MM_2004_16_7_a2
ER  - 
%0 Journal Article
%A A. S. Pavlov
%A L. F. Yukhno
%T On a solving ill-conditioned linear systems by iterative methods
%J Matematičeskoe modelirovanie
%D 2004
%P 13-20
%V 16
%N 7
%U http://geodesic.mathdoc.fr/item/MM_2004_16_7_a2/
%G ru
%F MM_2004_16_7_a2

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

The question of application of iterative conjugate gradients methods to solve ill-conditioned linear algebraic equations is discussed in this work. It is shown that for the arbitrary decisions these methods do not improve the precision in comparison with direct methods. Nevertheless for one main class that imitated non-orthogonal system expansion of function the concerned methods may get 5-6$^{\mathrm{th}}$ order of accuracy while direct ones can't get at least 1$^{\mathrm{th}}$.

[1] Kalitkin N. N., Kuzmina L. V., “Ob approksimatsii neortogonalnymi sistemami”, Matemat. modelirovanie, 16:3 (2004), 95–108 | MR | Zbl

[2] Faddee D. K., Faddeeva V. N., Vychislitelnye metody lineinoi algebry, Lan, S-Pet., 2002

[3] Abramov A. A., “Ob odnom metode resheniya plokho obuslovlennykh sistem lineinykh algebraicheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 31:4 (1991), 483–491 | MR

[4] Abramov A. A., Ulyanova V. I., Yukhno L. F., “O primenenii metoda Kreiga k resheniyu lineinykh uravnenii s netochno zadannymi iskhodnymi dannymi”, Zh. vychisl. matem. i matem. fiz., 42:12 (2002), 1763–1770 | MR | Zbl

[5] Samarskii A. A., Nikolaev E., Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR | Zbl

[6] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M., Chislennye metody, Laboratoriya Bazovykh Znanii, M., 2001

[7] Golub Dzh., Van Loun Ch., Matrichnye vychisleniya, Mir, M., 1999

[8] Craig E., “The $N$-step iteration procedures”, J. Math. and Phys., 34:1 (1955), 64–73 | MR | Zbl