Abstract: The Jacobi iterative method, Guass-Seidel iterative method, and SOR iterative method are commonly used in solving linear equations. When the coefficient matrix of a system of linear equations is strictly sub-diagonally dominant, we demonstrate that the Jacobi, Guass-Seider, and SOR iterative methods are all convergent. By comparing the upper bounds of error for the three iterative methods, we show that the upper bound of error for the Guass-Seidel iterative method is minimal.

Key words: linear equations, iterative method, strictly sub-diagonally dominant, error bounds