MSC2010 65F10, 65H10
On the continuous analogue of the Seidel method
I. V. Boikov1, A. I. Boikova2
| Annotation | Continuous Seidel method for solving systems of linear and nonlinear algebraic equations is constructed in the article, and the convergence of this method is investigated. According to the method discussed, solving a system of algebraic equations is reduced to solving systems of ordinary differential equations with delay. This allows to use rich arsenal of numerical ODE solution methods while solving systems of algebraic equations. The main advantage of the continuous analogue of the Seidel method compared to the classical one is that it does not require all the elements of the diagonal matrix to be non-zero while solving linear algebraic equations’ systems. The continuous analogue has the similar advantage when solving systems of nonlinear equations. |
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| Keywords | systems of algebraic equations, Seidel method, systems of ordinary differential equations, delay |
1Ilya V. Boikov, Head of Department of Higher and Applied Mathematics, Penza State University (40 Krasnaya St., Penza 440026, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0002-6980-933X, i.v.boykov@gmail.com
2Alla I. Boikova, Associate Professor, Department of Higher and Applied Mathematics, Penza State University (40 Krasnaya St., Penza 440026, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0002-6980-933X, allaboikova@mail.ru
Citation: I. V. Boikov, A. I. Boikova, "[On the continuous analogue of the Seidel method]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,20:4 (2018) 364–377 (In Russian)
DOI 10.15507/2079-6900.20.201804.364-377
