We discuss stationary iterative methods for tridiagonal matrix. Classical iterative methods such as the Jacobi method and the Gauss-Seidel method are well-known. These methods have the advantage of being simple algorithms. This effectiveness is obtained by a simple splitting of the coefficient matrix. However, for off-diagonally dominant, the convergence of the method is not guaranteed. In this paper, we propose a new iterative method based on the other decomposition utilizing the properties of tridiagonal matrix for the case where the Jacobi iterative method diverges.
