Further Study on (I+S_(max)) Preconditioning Gauss-Seidel Iterative Method

Hisashiki Kotakemori had proposed a preconditioner (I+S_(max)) for irreducibly diagonally dominant Z-matrix, which achieves better convergence rate than the classical Gauss-Seidel method and even better than Modified Gauss-Seidel method with preconditioner (I+S) under certain circumstances. We extend his convergence theorem to the case of H-matrix, and apply the preconditioner (I+S_(max)) to twice preconditioning for irreducible non-singular M-matrix, combining with another preconditioner (I+S). Numerical examples had been given to confirm that the convergence rate had been improved on considerably.