Geodesic
Probabilistic estimation of matrix condition number
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 1, pp. 28-34

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Ill-conditioned matrices of systems of linear algebraic equations with random error of the right-hand side vector considered. The condition number of the system matrix is investigated. It is shown that under some natural conditions the number $\nu$ may be significantly decreased.
Keywords: ill-conditioned matrix, condition number, vector of random error, distribution function. 
@article{VNGU_2018_18_1_a2,
     author = {V. S. Antyufeev},
     title = {Probabilistic estimation of matrix condition number},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {28--34},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2018_18_1_a2/}
}
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V. S. Antyufeev. Probabilistic estimation of matrix condition number. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 1, pp. 28-34. http://geodesic.mathdoc.fr/item/VNGU_2018_18_1_a2/