Solution of ill-conditioned system of linear algebraic equations
L. B. Bolotin1, E. B. Kuznetsov2
| Annotation | The paper deals with the numerical solution for a system of linear algebraic equations which are ill-conditioned for some values of the problem parameter. For example, the parameter may be time. The solution of such system according to Cramer's rule or the Gauss method, for example, is impossible in the vicinity of singularity of the system matrix. An offered algorithm allows to pass successfully the vicinity of the singularity and own singular point, where the system matrix degenerates. This algorithm involves the method of solution continuation with respect to the best parameter. |
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| Keywords | system of linear algebraic equations, method of solution continuation with respect to a parameter, the best continuation parameter, ordinary differential equations, initial value problem, numerical methods of integration |
1A student of the Department of differential equations, Moscow Aviation Institute, (national research university), Moscow; yourleo@yandex.ru,
2A professor of the Department of differential equations, Moscow Aviation Institute, (national research university), Moscow; kuznetsov@mai.ru
Citation: L. B. Bolotin , E. B. Kuznetsov , "[Solution of ill-conditioned system of linear algebraic equations]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:1 (2016) 7–11 (In Russian)
