Geodesic
Bounds on the transformed errors of solutions to SLAEs with ill-conditioned matrices
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 1979-1985 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Bounds on the norms of transformed relative errors of solutions to simultaneous linear algebraic equations (SLAEs) taking into account the influence of errors in the specification of the lefthand side matrix and the right-hand side vector for various types of regularization are obtained. These bounds are valid in a wide range of values of the initial data. 
@article{ZVMMF_2015_55_12_a0,
     author = {V. V. Godlevskii and V. S. Godlevskii},
     title = {Bounds on the transformed errors of solutions to {SLAEs} with ill-conditioned matrices},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1979--1985},
     year = {2015},
     volume = {55},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a0/}
}
TY  - JOUR
AU  - V. V. Godlevskii
AU  - V. S. Godlevskii
TI  - Bounds on the transformed errors of solutions to SLAEs with ill-conditioned matrices
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 1979
EP  - 1985
VL  - 55
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a0/
LA  - ru
ID  - ZVMMF_2015_55_12_a0
ER  - 
%0 Journal Article
%A V. V. Godlevskii
%A V. S. Godlevskii
%T Bounds on the transformed errors of solutions to SLAEs with ill-conditioned matrices
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 1979-1985
%V 55
%N 12
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a0/
%G ru
%F ZVMMF_2015_55_12_a0
V. V. Godlevskii; V. S. Godlevskii. Bounds on the transformed errors of solutions to SLAEs with ill-conditioned matrices. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 1979-1985. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a0/

[1] Petrov I. B., Lobanov A. I., Lektsii po vychislitelnoi matematike, BINOM. Laboratoriya znanii, M., 2006

[2] Verzhbitskii V. M., Osnovy chislennykh metodov, Vyssh. shkola, M., 2002

[3] Godlevskii B. C., “Ob otsenkakh zakonov raspredelenii pogreshnostei reshenii sistem lineinykh algebraicheskikh i obyknovennykh differentsialnykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 14:5 (1974), 1084–1092

[4] Lavrentev M. M., Savelev L. Ya., Teoriya operatorov i nekorrektnye zadachi, Izd-vo In-ta matematiki, Novosibirsk, 2010

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

[6] Wilkinson J. H., “A priori error analysis of algebraic processes”, Proc. International Congress Math. (Moscow, 1966), Mir Publishers, M., 1968 | MR