Open AccessOn the continuous analogue of the Seidel method
Author(s) -
И. В. Бойков,
И. В. Бойков
Publication year - 2018
Publication title -
žurnal srednevolžskogo matematičeskogo obŝestva
Language(s) - English
Resource type - Journals
eISSN - 2587-7496
pISSN - 2079-6900
DOI - 10.15507/2079-6900.20.201804.364-377
Subject(s) - mathematics , algebraic equation , nonlinear system , differential algebraic equation , ode , simultaneous equations , convergence (economics) , algebraic number , ordinary differential equation , system of linear equations , coefficient matrix , independent equation , diagonal , linear system , differential equation , mathematical analysis , eigenvalues and eigenvectors , physics , geometry , quantum mechanics , economic growth , economics
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.