A special shift splitting iteration method for absolute value equation

In this paper, based on the shift splitting (SS) technique, we propose a special SS iteration method for solving the absolute value equation (AVE), which is obtained by reformulating equivalently the AVE as a two-by-two block nonlinear equation. Theoretical analysis shows that the special SS method is absolutely convergent under proper conditions. Numerical experiments are given to demonstrate the feasibility, robustness and effectiveness of the special SS method.