Geodesic
A well-posed setting of the problem of solving systems of linear algebraic equations
Sbornik. Mathematics, Tome 213 (2022) no. 10, pp. 1436-1443 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Tikhonov's setting of the problem of solving systems of linear algebraic equations that are equivalent in accuracy is investigated. The problem is shown to be well posed in this setting. Bibliography: 5 titles.
Keywords: systems of linear algebraic equations, matrix norms, correct problems.
Mots-clés : normal pseudosolution 
@article{SM_2022_213_10_a4,
     author = {E. E. Tyrtyshnikov},
     title = {A~well-posed setting of the problem of solving systems of linear algebraic equations},
     journal = {Sbornik. Mathematics},
     pages = {1436--1443},
     year = {2022},
     volume = {213},
     number = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2022_213_10_a4/}
}
TY  - JOUR
AU  - E. E. Tyrtyshnikov
TI  - A well-posed setting of the problem of solving systems of linear algebraic equations
JO  - Sbornik. Mathematics
PY  - 2022
SP  - 1436
EP  - 1443
VL  - 213
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/SM_2022_213_10_a4/
LA  - en
ID  - SM_2022_213_10_a4
ER  - 
%0 Journal Article
%A E. E. Tyrtyshnikov
%T A well-posed setting of the problem of solving systems of linear algebraic equations
%J Sbornik. Mathematics
%D 2022
%P 1436-1443
%V 213
%N 10
%U http://geodesic.mathdoc.fr/item/SM_2022_213_10_a4/
%G en
%F SM_2022_213_10_a4
E. E. Tyrtyshnikov. A well-posed setting of the problem of solving systems of linear algebraic equations. Sbornik. Mathematics, Tome 213 (2022) no. 10, pp. 1436-1443. http://geodesic.mathdoc.fr/item/SM_2022_213_10_a4/

[1] V. V. Vasin, Foundations of the theory of ill-posed problems, Publishing house of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 2020, 312 pp. (Russian)

[2] S. I. Kabanikhin, Inverse and ill-posed problems, Sibirskoe Nauchnoe Izdatel'stvo, Novosibirsk, 2009, 457 pp. (Russian)

[3] A. N. Tikhonov and V. Y. Arsenin, Solutions of ill-posed problems, 2nd revised and augmented ed., Nauka, Moscow, 1979, 286 pp. ; English transl. of 1st ed., Scripta Series in Mathematics, V. H. Winston Sons, Washington, DC; John Wiley Sons, New York–Toronto, ON–London, 1977, xiii+258 pp. | MR | Zbl | MR | Zbl

[4] A. N. Tikhonov, A. S. Leonov and A. G. Yagola, Nonlinear ill-posed problems, 2nd revised and augmented ed., KURS, Moscow, 2017, 400 pp.; English transl. of 1st ed., v. 1, 2, Appl. Math. Math. Comput., 14, Chapman Hall, London, 1998, xxviii+386 pp. | MR | Zbl

[5] A. N. Tikhonov, “Approximate systems of linear algebraic equations”, Zh. Vychisl. Mat. Mat. Fiz., 20:6 (1980), 1373–1383 ; English transl. in Comput. Math. Math. Phys., 20:6 (1980), 10–22 | MR | Zbl | DOI