Enhansing an estimate of the rate of the Seidel method convergence

Abstract

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.