×
Shaydurov, V.; Petrakova, V.

Three-parameter regularization algorithm for pseudo-solution of non-compatible systems. (English) Zbl 07853994

Lobachevskii J. Math. 45, No. 1, 328-335 (2024).

MSC:

65Fxx Numerical linear algebra
65Jxx Numerical analysis in abstract spaces
65Nxx Numerical methods for partial differential equations, boundary value problems

Keywords:

linear algebraic equations; ill-conditioned and degenerate systems; regularization method; linear combinations of regularized solutions; normal pseudo-solution
Cite Review PDF
Full Text: DOI

References:

[1] Riley, J. D., Solving systems of linear equations with a positive definite symmetric but possibly ill-conditioned matrix, Math. Tables Aids Comput., 9, 96-101, 1956 · Zbl 0066.10102
[2] Fadeeva, V. N., Shift for systems with ill-conditioned matrices, Zh. Vychisl. Mat. Mat. Fiz., 5, 907-911, 1965
[3] Bakushinsky, A. B., Some properties of regularizing algorithms, Zh. Vychisl. Mat. Mat. Fiz., 8, 426-428, 1968 · Zbl 0196.17906
[4] Morozov, V. A., Regularization under high noise conditions, Zh. Vychisl. Mat. Mat. Fiz., 36, 13-21, 1996 · Zbl 0915.65044
[5] Ageev, A. L.; Vasin, V. V., On the convergence of the generalized residual method and its discrete approximations, Mat. Zap. Ural. Univ., 11, 3-18, 1979 · Zbl 0456.65028
[6] Vasin, V. V., Optimality in order of the regularization method for nonlinear operator equations, Zh. Vychisl. Mat. Mat. Fiz., 17, 847-858, 1977 · Zbl 0358.47041
[7] Lavrent’ev, M. M., On improving the accuracy of solving a system of linear equations, Dokl. Akad. Nauk SSSR, 92, 885-886, 1953 · Zbl 0051.34604
[8] Lavrent’ev, M. M., On integral equations of the first kind, Dokl. Akad. Nauk SSSR, 127, 31-33, 1959 · Zbl 0107.09904
[9] Maslov, V. P., Existence of a solution to an ill-posed problem of an equivalently regularized process, Usp. Mat. Nauk, 23, 183-184, 1968 · Zbl 0167.42803
[10] P. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems (Nauka, Moscow, 1979; Halsted, New York, 1977). · Zbl 0354.65028
[11] E. E. Tyrtyshnikov, ‘‘Correct statement of the problem of solving systems of linear algebraic equations,’’ Mat. Sb. 213(10) (2022).
[12] Kabanikhin, S. I., Inverse and Ill-Posed Problems, 2009, Novosibirsk: Sib. Nauch. Izdat, Novosibirsk · Zbl 1170.35100
[13] Nazimov, A. B.; Morozov, V. A.; Mukhamadiev, E. M.; Mullodzanov, M., Method of Regularization by Shifting, 2012, Vologda: Volog. Tech. Univ., Vologda
[14] Shaydurov, V.; Kabanikhin, S.; Petrakova, V., Two algorithms for refinement of approximate solutions in the regularization method, Lobachevskii J. Math., 44, 437-445, 2023 · Zbl 1515.15006 · doi:10.1134/S1995080223010353
[15] G. I. Marchuk and V. V. Shaidurov, Improving the Accuracy of Solutions to Difference Schemes (Nauka, Moscow, 1979; Springer, Heidelberg, 1983). · Zbl 0496.65046
[16] Penrose, R., On best approximate solutions of linear matrix equations, Proc. Cambridge Philos. Soc., 52, 17-19, 1956 · Zbl 0070.12501 · doi:10.1017/S0305004100030929
[17] A. A. Samarskii and V. B. Andreev, Finite Difference Methods for Elliptic Equations (Nauka, Moscow, 1976; Science Press, Beijing, 1984). · Zbl 1310.35004
[18] Richardson, L. F., “The deferred approach to the limit. Single lattice,” Philos. Trans. R. Soc. London, Ser. A, 226, 299-349, 1927 · JFM 53.0432.01
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.