A New Class AOR Preconditioner for $L$-Matrices
Received:February 26, 2018  Revised:August 12, 2018
Key Word: AOR iterative method   $L$-matrix   irreducible matrix   spectral radius   preconditioner   iteration matrix
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 Author Name Affiliation Reza BEHZADI Department of Mathematics, College of Science, Shiraz University, Shiraz, Iran
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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.