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

Abstract In this paper, we obtain bounds for the spectral radius of the matrix l ω , 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.