Note on Irreducible Diagonally Dominant Matrices and the Convergence of the AOR Iterative Method
M. Madalena Martins · Mathematics of Computation · 1981
Considering the linear systems $Ax = b$, where the matrix A is irreducible and diagonally dominant, we obtain bounds for the spectral radius of the ${L_{r,\omega }}$ 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 $\omega$ of the SOR method, and we improve the results of Theorems 5, 6 of [3] for the AOR method.