A modified generalized SOR-like method for solving an absolute value equation

In this paper, we propose a modified generalized SOR-like (MGSOR) method for solving an absolute value equation (AVE), which is obtained by reformulating equivalently AVE as a two-by-two block nonlinear equation and by introducing the transformation Py := vertical bar x vertical bar with a general nonsingular matrix P. The convergence results of the MGSOR method are obtained under certain assumptions imposed on the involved parameters. Furthermore, the optimal parameters minimizing the convergence rate of the MGSOR method for solving AVE are studied in detail. Numerical experiments further illustrate that the MGSOR method is efficient and has better performance than some existing iteration methods in aspects of the number of iteration steps and CPU time.