Abstract: The paper presents a new effective preconditioned method and discusses some important properties of the new preconditioned method, and then, shows that the new preconditioned method can accelerate the convergence of Jacobi and Gauss-Seidel iterations for strictly diagonally dominant irreducible Z-matrices. Some comparison
theorems proved in the paper generalized some known results. Some numerical examples illustrate its validity.

Key words: Spectral radius, Preconditioned method, Strictly diagonally dominant, Z-matrix