A New Class AOR Preconditioner for $L$-Matrices

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 ∈ R~(n×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.