[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 |