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 ∈ Rn×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.
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