The article discusses the Seidel method for solving a system of linear algebraic equations and an estimate of the rate of the Seidel method convergence. It is proposed to construct an equivalent system for which the Seidel method also converges, but the rate of convergence is better. An equivalent system is constructed by a separate iterative process, where each single step requires O(n) operations. Stability of this iterative process is proved. Results of numerical experiments are presented showing an improvement of the estimate of the rate of convergence.
Original languageRussian
Pages (from-to)185-195
JournalВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. МАТЕМАТИКА. МЕХАНИКА. АСТРОНОМИЯ
Volume6
Issue number2
StatePublished - 2019
Externally publishedYes

    Research areas

  • estimate of the rate of the Seidel method convergence, Iterative solution methods, one-step cyclic process, Seidel method, Seidel method convergence, SLAE, system of linear algebraic equations, итерационные методы решения, метод Зейделя, одношаговый циклический процесс, оценка скорости сходимости метода Зейделя, система линейных алгебраических уравнений, СЛАУ, сходимость метода Зейделя

ID: 78390742