The recent convergence results of faster group iterative schemes from the Accelerated OverRelaxation (AOR) family has initiated considerable interest in exploring the ehavior of these methods in the solution of partial differential equations (pdes). Martins et al. (2002) formulated the Explicit Group (EG) (AOR) which was shown to have greater rate of convergence than the standard five-point AOR...

Based on the work of Wang and Li [A new preconditioned AOR iterative method for L-matrices, J. Comput. Appl. Math. 229 (2009) 47-53], in this paper, a new preconditioner for the AOR method is proposed for solving linear systems whose coefficient matrix is an L-matrix. Several comparison theorems are shown for the proposed method with two preconditioners. It follows from the comparison results t...

In this paper, we will present a modification of the preconditioned AOR-type method for solving the linear system. A theorem is given to show the convergence rate of modification of the preconditioned AOR methods that can be enlarged than the convergence AOR method.

‎In this paper‎, ‎we propose two preconditioned AOR iterative methods to solve systems of linear equations whose coefficient matrices are Z-matrix‎. ‎These methods can be considered as improvements of two previously presented ones in the literature‎. ‎Finally some numerical experiments are given to show the effectiveness of the proposed preconditioners‎.‎

We study the semiconvergence of Gauss-Seidel iterative methods for the least squares solution of minimal norm of rank deficient linear systems of equations. Necessary and sufficient conditions for the semiconvergence of the Gauss-Seidel iterative method are given. We also show that if the linear system of equations is consistent, then the proposed methods with a zero vector as an initial guess ...

Non-stationary parallel multisplitting iterative methods based on the AOR method are studied for the solution of nonsingular linear systems. Convergence of the synchronous and asyn-chronous versions of these methods is studied for H–matrices. Furthermore, computational results about these methods on both shared and distributed memory multiprocessors are discussed. The numerical examples present...

In this paper we consider the parallel generalized SAOR iterative method based on the generalized AOR iterative method presented by James for solving large nonsingular system. We obtain some convergence theorems for the case when coefficient matrix is a block diagonally dominant matrix or a generalized block diagonal dominant matrix. A numerical example is given to illustrate to our results. Cr...