Improving preconditioned SOR-type iterative methods for L-matrices
Mehdi Dehghan, Masoud Hajarian · International Journal for Numerical Methods in Biomedical Engineering · 2009
The preconditioned methods are often used to accelerate the convergence of the iterative methods for solving linear system Ax=b. So far, several preconditioners have been presented and used for solving linear system Ax=b under strong assumptions on A. In this paper, we propose two new preconditioner techniques to solve L-matrices linear system and analyze their convergence properly. From the comparison theorems, we can conclude that the proposed preconditioner techniques can be applied to accelerate the convergence of the successive over-relaxation (SOR) iterative method under mild assumptions on A. Several numerical examples are presented to support the theoretical results of this paper. Copyright © 2009 John Wiley & Sons, Ltd.