| A New Class AOR Preconditioner for $L$-Matrices |
| Received:February 26, 2018 Revised:August 12, 2018 |
| Key Words:
AOR iterative method $L$-matrix irreducible matrix spectral radius preconditioner iteration matrix
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| Abstract: |
| Hadjidimos (1978) proposed a classical accelerated overrelaxation (AOR) iterative method to solve the system of linear equations, and discussed its convergence under the conditions that the coefficient matrices are irreducible diagonal dominant, $L$-matrices, and consistently orders matrices. Several preconditioned AOR methods have been proposed to solve system of linear equations $Ax = b$, where $A \in \mathbb{R}^{n\times n}$ is an $L$-matrix. In this work, we introduce a new class preconditioners for solving linear systems and give a comparison result and some convergence result for this class of preconditioners. Numerical results for corresponding preconditioned GMRES methods are given to illustrate the theoretical results. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2019.01.010 |
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