Abstract—In this paper, we present preconditioned generalized accelerated overrelaxation (GAOR) methods for solving certain nonsingular linear system. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GAOR methods converge faster than the GAOR method whenever the GAOR method is convergent. ...

We present preconditioned generalized accelerated overrelaxation methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GAOR methods converge faster than the GAOR method whenever the GAOR method is convergent. Finally, we give a numerica...

Recently, some convergent results of the generalized AOR iterative (GAOR) method for solving linear systems with strictly diagonally dominant matrices are presented in [Darvishi, M.T., Hessari, P.: On convergence of the generalized AOR method for linear systems with diagonally dominant cofficient matrices. Appl. Math. Comput. 176, 128-133 (2006)] and [Tian, G.X., Huang, T.Z., Cui, S.Y.: Converg...

Three kinds of preconditioners are proposed to accelerate the generalized AOR (GAOR) method for the linear system from the generalized least squares problem. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned generalized AOR (PGAOR) methods is better than that of the original GAOR methods. Finally, some numerical resu...

In this paper, we study the convergence of the generalized accelerated overrelaxation (GAOR) iterative method. That is an extension of the classical convergence result of the generalized successive overrelaxation (GSOR) iterative method. We proposed some theorems, which they obtain better results than similar works. By some numerical examples we show the goodness of our results. 2006 Elsevier I...