On convergence of preconditioned Gauss-Seidel iterative method

The preconditioned Gauss-Seidel iterative method is introduced. It is proved that if the coefficient matrix is an irreducible Z-matrix, H-matrix or positive definite matrix, then the preconditioned Gauss-Seidel iterative method is convergent. Thus it expands the applicable scope of the method. Finally, a simple numerical example shows the validity of the conclusions.