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

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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 
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/
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[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