MSC2010 65F22
Gauss method application to solution of ill-conditioned systems of linear algebraic equations
L. B. Bolotin1, E. B. Kuznetsov2
| Annotation | The paper deals with the numerical solution of the system of linear algebraic equations that is singular under certain values of the problem parameter, which can be, for example, time. The solution of such system by the Kramer's rule or using the method of Gauss is impossible in the neighborhood of singularity of the system matrix. The algorithm which can successfully overcome the neighborhood of the singularity and singular points in which the matrix of the system degenerates is proposed. The algorithm implies the application of the method of solution continuation with respect to the best parameter and Gauss method of solution of linear algebraic equations system. |
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| Keywords | system of linear algebraic equations, singular points, method of solution continuation with respect to a parameter, the best parameter of continuation, numerical methods, ordinary differential equations |
1Leonid B. Bolotin, student, Department of differential equations, Moscow Aviation Institute (National Research University) (125993, Russia, Moscow, Volokolamskoe Shosse, 4.), ORCID: http://orcid.org/0000-0002-0135-317X, yourleo@yandex.ru
2Evgeny B. Kuznetsov, Professor, Department of differential equations, Moscow Aviation Institute (National Research University) (125993, Russia, Moscow, Volokolamskoe Shosse, 4.), Dr. Sci. (Phys.-Math.), ORCID: http://orcid.org/0000-0002-0135-317X, kuznetsov@mai.ru
Citation: L. B. Bolotin, E. B. Kuznetsov, "[Gauss method application to solution of ill-conditioned systems of linear algebraic equations]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,19:1 (2017) 13–18 (In Russian)
DOI 10.15507/2079-6900.19.2017.01.13-18
