An Efficient Algorithm for Solving Absolute Value Equations

Recently, absolute value equations (AVEs) are lied in the consideration center of some researchers since they are very suitable alternatives for many frequently occurring optimization problems. Therefore, finding a fast solution method for these type of problems is very significant. In this paper, based on the mixed-type splitting (MTS) idea for solving linear system of equations, a new fast algorithm for solving AVEs is presented. This algorithm has two auxiliary matrices which are limited to be nonnegative strictly lower triangular and nonnegative diagonal matrices. The convergence of the algorithm is discussed via some theorems. In addition, it is shown that by suitable choice of the auxiliary matrices, the convergence rate of this algorithm is faster than that of the SOR, AOR, Generalized Newton, Picard and SOR-like methods. Eventually, some numerical results for different size of problem dimensionality are presented which admit the credibility of the proposed algorithm.