Improving an Estimate of the Convergence Rate of the Seidel Method

  • A. N. BorzykhEmail author


The Seidel method for solving a system of linear algebraic equations and an estimate of the rate of its convergence are considered in this paper. It is proposed to construct an equivalent system for which the Seidel method also converges but yields a better rate of convergence. An equivalent system is constructed by a separate iterative process, where each step requires O(n) operations. The stability of this process is proved. Results of numerical experiments are presented that show an improvement in the estimate of the convergence rate.


Seidel method one-step cyclic process SLAE system of linear algebraic equations iterative solution methods convergence of the Seidel method estimate of the convergence rate of the Seidel method 


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  1. 1.
    D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra (Lan’, St. Petersburg, 2002) [in Russian].zbMATHGoogle Scholar
  2. 2.
    A. N. Borzykh, “Improving an estimate of the convergence rate of the Seidel method by selecting the optimal order of equations in the system of linear algebraic equations,” Comput. Math. Math. Phys. 57, 1–6 (2017). MathSciNetCrossRefzbMATHGoogle Scholar

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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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