Abstract
Regularization of singular systems of linear algebraic equations by shifts is examined. New equivalent conditions for the shift regularizability of such systems are derived.
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A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems (Halsted, New York, 1977; Nauka, Moscow, 1979).
V. A. Morozov, Regular Methods for Solving Ill-Posed Problems (Mosk. Gos. Univ., Moscow, 1974) [in Russian].
A. B. Bakushinskii, Selected Topics of Approximate Solution of Ill-Posed Problems (Mosk. Gos. Univ., Moscow, 1968) [in Russian].
V. A. Trenogin and N. A. Sidorov, “On the Tikhonov Regularization of the Problems of Bifurcation Points of Non-linear Operators,” Sib. Mat. Zh. 17, 402–413 (1976).
I. K. Lifanov, “On the Ill-Posedness and Regularization of the Numerical Solution to Singular Integral Equations,” Dokl. Akad. Nauk SSSR 255, 1046–1050 (1980).
F. R. Gantmacher, The Theory of Matrices (Chelsea, New York, 1959; Nauka, Moscow, 1966).
V. A. Morozov and A. B. Nazimov, “On the Regularization of Sets of Linear Algebraic Equations,” Dokl. Akad. Nauk SSSR 286, 286–289 (1986).
V. A. Morozov and A. B. Nazimov, “The Necessary and Sufficient Conditions of the Regularizability of Degenerate Sets of Linear Algebraic Equations Using the Shift Method,” Zh. Vychisl. Mat. Mat. Fiz. 26, 1283–1290 (1986).
B. P. Demidovich and I. A. Maron, Computational Mathematics (Mir, Moscow, 1973; Lan’, St. Petersburg, 2006).
A. B. Bakushinskii and A. V. Goncharskii, Iterative Methods for Solving Ill-Posed Problems (Nauka, Moscow, 1989) [in Russian].
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Original Russian Text © V.A. Morozov, E.M. Mukhamadiev, A.B. Nazimov, 2007, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2007, Vol. 47, No. 12, pp. 1971–1978.
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Morozov, V.A., Mukhamadiev, E.M. & Nazimov, A.B. Regularization of singular systems of linear algebraic equations by shifts. Comput. Math. and Math. Phys. 47, 1885–1892 (2007). https://doi.org/10.1134/S0965542507120019
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DOI: https://doi.org/10.1134/S0965542507120019