Abstract :

Solving Systems Of Linear Equations Is Central To Numerous Scientific And Engineering Applications. Iterative Methods Like Jacobi, Gauss-Seidel, And Successive Over-Relaxation (SOR) Are Widely Used For Large Sparse Systems. This Paper Explores The Theoretical Foundations And Practical Applications Of The SOR Method, Comparing Its Performance To Jacobi And Gauss-Seidel Methods. A Numerical Example Is Solved Using All Three Methods. Furthermore, We Explore How Artificial Intelligence (AI) Techniques Can Enhance The Performance Of SOR By Optimizing The Relaxation Factor ?, Thereby Improving Convergence. Keywords: Successive Over-Relaxation, Gauss-Seidel Method, Jacobi Method, Iterative Solvers, Artificial Intelligence, Machine Learning, Convergence Analysis, Computational Efficiency, Numerical Approximation, Hybrid Algorithms

Published:

25-9-2025

Issue:

Vol. 25 No. 9 (2025)

Page Nos:

356-358

Section:

Articles

License:

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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