We consider ill-conditioned matrices of systems of linear algebraic equations with random error of vector right-hand side. We study the condition number ν of the matrix of the system. We show that, under certain natural assumptions, the number ν can be considerably diminished. Bibliography: 3 titles. Illustrations: 3 figures.
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R. Bellman, Introduction to Matrix Analysis, McGrow-Hill, New York etc. (1960).
W. Feller, An Introduction to Probability Theory and Its Applications, John Wiley and Sons, New York etc. (1970).
G. M. Fikhtengolts, Course of Differential and Integral Calculus [in Russian], Nauka, Moscow (1977).
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Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki18, No. 1, 2018, pp. 28-34.
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Antyufeev, V.S. Probabilistic Estimation of Matrix Condition Number. J Math Sci 246, 755–762 (2020). https://doi.org/10.1007/s10958-020-04778-1
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DOI: https://doi.org/10.1007/s10958-020-04778-1