Convergence analysis of the preconditioned Gauss-Seidel method for H-matrices

113–123] proved that the convergence rate of the preconditioned Gauss–Seidel method for irreducibly diagonally dominant Z-matrices with a preconditioner I + S α is superior to that of the basic iterative method. In this paper, we present a new preconditioner I + K β which is different from the preconditioner given by Kohno et al. and prove the convergence theory about two preconditioned iterative methods when the coefficient matrix is an H-matrix. Meanwhile, two novel sufficient conditions for guaranteeing the convergence of the preconditioned iterative methods are given.