Some techniques for solving absolute value equations

In this paper, we introduce and analyze two new methods for solving the NP-hard absolute value equations (AVE) Ax−|x|=b,Ax−|x|=b, where A is an arbitrary n × n real matrix and b ∈ Rn, in the case, singular value of A exceeds 1. The comparison with other known methods is carried to show the effectiveness of the proposed methods for a variety of randomly generated problems. The ideas and techniques of this paper may stimulate further research.