Considering the linear systems
A
x
=
b
Ax = b
, where the matrix A is irreducible and diagonally dominant, we obtain bounds for the spectral radius of the
L
r
,
ω
{L_{r,\omega }}
matrix of the AOR method and we achieve the convergence conditions given in [2] by a different method. If A is strictly diagonally dominant, we get larger intervals for the parameter
ω
\omega
of the SOR method, and we improve the results of Theorems 5, 6 of [3] for the AOR method.