Study of Matrix Iteration Methods for Solving Large-Scale Linear Systems

Abstract

Matrix iteration methods are powerful numerical techniques used to solve large systems of linear equations, especially where direct methods become computationally expensive. This paper investigates the efficiency, convergence behavior, and accuracy of key iterative techniques such as the Jacobi Method, Gauss-Seidel Method, and Successive Over-Relaxation (SOR) Method. Emphasis is placed on their application in engineering and scientific problems involving sparse and large matrices. Numerical experiments are conducted to compare performance based on iteration count, computational time, and error norms. The study provides practical guidelines for selecting appropriate methods depending on matrix properties such as diagonal dominance and sparsity. The results demonstrate that while no single method is universally superior, optimized parameter choices and hybrid approaches can significantly enhance solution efficiency for specific classes of problems.

Cite as:

Awasare Anant, & P. Thorat. (2025). Study of Matrix Iteration Methods for Solving Large-Scale Linear Systems. Journal of Applied Mathematics and Statistical Analysis, 6(2), 32–37. 

https://doi.org/10.5281/zenodo.16411693