Generalized Jacobi and Gauss-Seidel Methods for Solving Linear System of Equations

respectively. There are many iterative methods such as GMRES [7] and Bi-CGSTAB [9] algorithms for solving Eq. (1.1) which are more efficient than the Jacobi and Gauss-Seidel methods. However, when these methods are combined with the more efficient methods, for example as a preconditioner, can be quite successful. For example see [4, 6]. It has been proved that if A is a strictly diagonally dominant (SDD) or irreducibly diagonally dominant, then the associated Jacobi and Gauss-Seidel iterations converge for any initial guess x0 [6]. If A is a symmetric positive definite (SPD) matrix, then the Gauss-Seidel Corresponding author.