On convergence of the generalized AOR method for linear systems with diagonally dominant coefficient matrices

In this paper, we obtain bounds for the spectral radius of the matrix ℓω,r, which is the iterative matrix of generalized accelerated overrelaxation (GAOR) iterative method. We consider a linear system Hy = f, where H is an n × n diagonally dominant real matrix, f is an n-real vector of known values and y is an n-real vector of unknown variables. Sufficient conditions for the convergence of GAOR method will be presented.