A new modified preconditioned accelerated overrelaxation (AOR) iterative method for L-Matrix linear algebraic systems

A new preconditioner of the type =+̅+′ which generalizes the preconditioners of Evans et al. (2001) and Ndanusa and Adeboye (2012) is proposed. Theoretical investigation of the new preconditioned AOR method is undertaken by advancement of some convergence theorems with well-known procedures. In order to validate the results of theoretical convergence analysis, numerical investigation with sample problems is done. Numerical results of comparison of the proposed preconditioner with some available preconditioners in literature are presented. The results show that convergence of the proposed preconditioned AOR method is faster than that of the unpreconditioned AOR as well as the preconditioned methods in current use

An Adaptive Preconditioner Matrix on N-P Group AOR Iterative Poisson Solver

Hadjidimos [1], proved that the Accelerated OverRelaxation (AOR) is more powerful compared with the other well-known method called the Successive OverRelaxation (SOR) for solving linear systems of equations. The formulation of group iterative schemes for approximating the solution of the two dimensional elliptic partial differential equations have been the subject of intensive study during the last few years. The recent convergence results of nine-point (N-P) group iterative schemes from the Successive OverRelaxation (SOR) family have been presented by Saeed [2]. In this paper, we extend the work of Saeed [2] with the new application of suitable preconditioning techniques to the N-P Group iterative schemes from the Accelerated OverRelaxation (AOR) for solving Poisson’s Equation. The results reveal the significant improvement in number of iterations and execution timings of the proposed preconditioned Group iterative method compared to Preconditioned N-P SOR

Modified Preconditioned GAOR Methods for Systems of Linear Equations

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 results are reported to confirm the validity of the proposed methods

A New Preconditioner on Gauss‐Seidel Method for H‐Matrices

In order to accelerate the convergency of Gauss‐Seidel method to solve systems of linear equations when the coefficient matrix is an H‐matrix, a new preconditioner is introduced. The convergency of the new preconditioned method is proved

A variant of the AOR method for augmented systems

A variant of the AOR method for augmented system