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A preconditioned AOR iterative method for the absolute value equations. (English) Zbl 1404.65052

Summary: In this paper, coupled with a preconditioning technique, a preconditioned accelerated over relaxation (PAOR) iterative method for solving the absolute value equations (AVEs) is presented. Some comparison theorems are given when the matrix of the linear term is an irreducible \(L\)-matrix. Comparison results show that the convergence rate of the PAOR iterative method is better than that of the accelerated over relaxation (AOR) iterative method whenever both are convergent. Numerical experiments are provided in order to confirm the theoretical results studied in this paper.

MSC:

65K05 Numerical mathematical programming methods
65F10 Iterative numerical methods for linear systems
65F08 Preconditioners for iterative methods
90C05 Linear programming
90C30 Nonlinear programming
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