In this paper, to improve the convergence speed of the block-diagonal and anti-block-diagonal splitting (BAS) iteration method, we design a modified BAS (MBAS) method to obtain the numerical solution of the absolute value equation. Theoretical analysis shows that under certain conditions the MBAS method is convergent. Numerical experiments show that the MBAS method is feasible.

In this paper, based on the accelerated over relaxation (AOR) iteration method, a generalization of the AOR iteration method is presented to solve the absolute value equations (AVE), which is called the GAOR method. The convergence conditions of the GAOR method are obtained. Numerical experiments are presented in order to verify the feasibility of the GAOR method.