COMPARATIVE ANALYSIS OF GAUSS SEIDEL, CONJUGATE GRADIENT AND SUCCESSIVEOVER RELAXATION FOR THE SOLUTION OF NONSYMETRIC LINEAR EQUATIONS

الملخص

This study undertakes a comparative analysis of three widely used computational methods namely; Gauss-Seidel, Conjugate Gradient, and Successive Over-Relaxation (SOR) for solving nonsymmetric linear equations. The main goal is to assess the effectiveness, efficiency and convergence rates of these methods when applied to nonsymmetric linear systems, which frequently occurs in scientific and engineering problems. The Gauss-Seidel method, known
for its iterative simplicity and straightforward implementation, is compared with the Conjugate Gradient method, which is acclaimed for its robustness and efficiency in handling large and sparse systems. The SOR method, an optimized version of Gauss-Seidel, was also evaluated to determine its potentials for accelerating convergence. Through a series of numerical experiments and performance benchmarks, the study reveals that the Conjugate
Gradient method consistently outperforms the other two methods in terms of convergence, speed and computational efficiency, particularly for large-scale nonsymmetric systems. The Gauss-Seidel and SOR methods, while showing competitive performance for smaller or less complex systems, do not match the efficiency of the Conjugate Gradient method in more demanding scenarios. Based on the results, the Conjugate Gradient method is recommended as the preferred choice for solving large nonsymmetric linear systems due to its superior performance.