A Comparative Study Of Two Iterative Techniques For Systems Of Linear Algebraic Equations

Abstract

This study compares numerically two iterative methods for solving systems of linear algebraic equations: the Symmetric Accelerated Overrelaxation technique and the Symmetric Successive Overrelaxation method. Four numerical problems are applied to analyze and compare the convergence speeds of the two approaches. On the basis of performance metrics including spectral radius, convergence time, accuracy, and number of iterations required to converge, the numerical results demonstrate that the Symmetric Accelerated Overrelaxation approach needed less computing time, a smaller spectral radius, and fewer iterations than the Symmetric Successive Overrelaxation approach. This demonstrates that the Symmetric Accelerated Overrelaxation is superior to the Symmetric Successive Overrelaxation. Researchers and numerical analysts can benefit from the findings of this study; it will help them comprehend iteration techniques and adopt an appropriate or more efficient iterative strategy for solving systems of linear algebraic equations.