Abstract
Statistical estimates with respect to observations over the coefficient matrix of the system of equations are found for the regularized solutions of systems of linear algebraic equations. Under certain conditions, it is proved that this estimate is asymptotically normal.
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V. L. Girko, Theory of Random Determinants [in Russian], Vishcha Shkola, Kiev (1980).
T. Kato, Perturbation Theory for Linear Operators, Springer Verlag, Berlin—New York (1966).
F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1967).
V. L. Girko, “On the distribution of solutions of a system of linear equations with random coefficients,” Teor. Veroyatn. Mat. Stat., No. 2, 41–44 (1970).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 6, pp. 755–762, June, 1990.
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Girko, V.L. Asymptotically normal estimates of solutions of systems of linear algebraic equations. I. Ukr Math J 42, 666–671 (1990). https://doi.org/10.1007/BF01058909
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DOI: https://doi.org/10.1007/BF01058909