PERBANDINGAN METODE ITERASI GAUSS-SEIDEL DAN JACOBI IMPLEMENTASI DAN SIMULASI MENGGUNAKAN MATLAB
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Iteration Method,
Gauss-Seidel,
Jacobi,
MATLAB Simulation
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Abstract
The system of linear equations is one of the main foundations in various science and technology applications, which is often solved using iterative methods such as Jacobi and Gauss-Seidel methods. This study aims to compare the two methods in terms of convergence speed, solution stability, and computational time efficiency. Simulations were conducted using MATLAB with a quantitative experimental approach on a diagonally dominant system of linear equations, which confirmed the convergence potential of the iterative methods. The implementation of the algorithm involves using the same initial values for both methods, with the process iterating until it reaches the convergence criterion or maximum limit of iterations. Simulation results show that the Gauss-Seidel Method is superior in convergence speed, requiring only 11 iterations to reach a solution, compared to 21 iterations in the Jacobi Method. In addition, the Gauss-Seidel Method shows better stability on the tested system, while the Jacobi Method has an advantage in the flexibility of parallel implementation. These findings provide important insights for users to choose numerical methods that suit specific needs, both in academic contexts and practical applications, especially for solving systems of linear equations in modern computing.
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