Relaxed-based matrix splitting methods for solving absolute value equations

In this paper, we investigate the iterative methods for solving the absolute value equations (AVEs). Using matrix splitting and the relaxed technique, a relaxed-based matrix splitting (RMS) method is presented. As special cases, we propose a relaxed-based Picard (RP) method, relaxed-based AOR (RAOR) method, and relaxed-based SOR (RSOR) method. These methods include some known methods as special cases, such as the Newton-based matrix splitting iterative method, the modified Newton type iteration method, the Picard method, a new SOR-like method, the fixed point iteration method, the SOR-like method, the AOR method, the modified SOR-like method, etc. Some convergence conditions of the proposed method are presented. Numerical examples verify the theoretical results and the advantages of the new methods.