Optimum Accelerated Overrelaxation Method
نویسندگان
چکیده
In this paper we give the optimum parameters for the Accelerated Overrelaxation (AOR) method in the special case where the matrix coefficient of the linear system, which is solved, is consistently ordered with nonvanishing diagonal elements. Under certain assumptions, concerning the eigenvalues of the corresponding Jacobi matrix, it is shown that the optimum AOR method gives better convergence rates than the optimum SOR does, while in the remaining cases the optimum AOR method coincides with the optimum SOR one.
منابع مشابه
On the Solution of the Linear Complementarity Problem by the Generalized Accelerated Overrelaxation Iterative Method
In the present work, we determine intervals of convergence for the various parameters involved for what is known as the Generalized Accelerated Overrelaxation iterative method for the solution of the Linear Complementarity Problem. The convergence intervals found constitute sufficient conditions for the Generalized Accelerated Overrelaxation method to converge and are better than what have been...
متن کاملOn convergence of the generalized accelerated overrelaxation method
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...
متن کاملThe Best Values of Parameters in Accelerated Successive Overrelaxation Methods
In this paper we find the best values of parameters in accelerated successive overrelaxation method (ASOR). We state and prove some theorems that show how we can find the optimal values of parameters in ASOR for special coefficient matrices. Key-Words: Linear systems, iterative methods, relaxation, ASOR.
متن کاملSome Results on Preconditioned Modified Accelerated Overrelaxation Method
In this paper, we present new preconditioned modified accelerated overrelaxation (MAOR) method for solving linear systems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned MAOR method converges faster than the MAOR method whenever the MAOR method is convergent. Finally, we give one numeric...
متن کاملAccelerated Overrelaxation Method
This paper describes a method for the numerical solution of linear systems of equations. The method is a two-parameter generalization of the Successive Overrelaxation (SOR) method such that when the two parameters involved are equal it coincides with the SOR method. Finally, a numerical example is given to show the superiority of the new method.
متن کامل