<![CDATA[Iterative methods provide an efficient approach for solving large-scale systems of linear equations. This study aims to analyze the convergence and efficiency of the Gauss-Seidel method in solving linear systems through Maple-based implementation. Convergence analysis is conducted by examining the spectral radius of the iteration matrix and the diagonal dominance property of the coefficient matrix, while efficiency is evaluated based on the number of iterations and computational time. Numerical experiments are performed on various matrix sizes with an error tolerance of 10-5. The results indicate that the Gauss-Seidel method converges when the spectral radius of the iteration matrix is less than one and the coefficient matrix satisfies diagonal dominance conditions. The implementation in Maple enables systematic and accurate numerical and spectral analysis. This study contributes to computational-based numerical method analysis and provides a reference for selecting efficient iterative methods.]]>
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