Note on irreducible diagonally dominant matrices and the convergence of the AOR iterative method

Abstract

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.