2016•American Journal of Computational and Applied MathematicsOpen access

Refined Iterative Method for Solving System of Linear Equations

Genanew Gofe Gonfa

Abstract

In this paper, the refined iterative method namely, refinement of generalized Gauss-Seidel (RGGS) method for solving systems of linear equations is studied. Sufficient conditions for convergence are given and some numerical experiments are considered to show the efficiency of the method. The result shows that RGGS method converges if the coefficient matrix is diagonally dominant (DD) or an M- matrix for any initial vectors, moreover it is more efficient than the other methods Refinement of generalized Jacobi (RGJ) and successive-over relaxation (SOR) methods, considering their performance, using parameters such as time to converge, number of iterations required to converge and level of accuracy.

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Key concepts: Gauss–Seidel method, Relaxation (psychology), Coefficient matrix, Jacobi method, Mathematics, Iterative method, Successive over-relaxation, Convergence (economics)