Guangbin Wang

Convergence of GAOR method for doubly diagonally dominant matrices

Abstract In this paper, we obtain bounds for the spectral radius of the matrix l ω , r which is the iterative matrix of the generalized accelerated overrelaxation (GAOR) iterative method. Moreover, we present one convergence theorem of the GAOR method. Finally, we present two numerical examples.

Some results on preconditioned GAOR methods

In this paper, we present preconditioned generalized accelerated overrelaxation methods. We compare the spectral radii of the iteration matrices of the preconditioned and 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 present two numerical examples to confirm our theoretical results.

Convergence of GAOR Iterative Method with Strictly α Diagonally Dominant Matrices

We discuss the convergence of GAOR method for linear systems with strictly α diagonally dominant matrices. Moreover, we show that our results are better than ones of Darvishi and Hessari (2006), Tian et al. (2008) by using three numerical examples.

Some results on a generalized alternating iterative method

Climent and Perea [J.-J. Climent, C. Perea, Convergence and comparison theorems for a generalized alternating iterative method, Appl. Math. Comput. 143 (2003) 1-14] introduced a generalized alternating iterative method. In this paper, we establish convergence results for a nonsingular H-matrix, upper bound to the spectral radius of iterative matrix and comparison theorem for a monotone matrix. Moreover, we give some numerical examples to show our results.

Preconditioned parallel multisplitting USAOR method for H-matrices linear systems

In this paper, the preconditioned multisplitting USAOR method is established for solving the system of linear equations. The convergence and comparison results of the method are given when the coefficient matrices of the linear systems are H-matrices. The method for H-matrices is proved to be more efficient than the multisplitting USAOR method for M-matrices. Finally, a numerical example is given to illustrate the efficiency of our method.