In this paper, we propose a fast convergent two-step iterative algorithm to solve the NP-hard absolute value equation when the solution is unique. Our method is based on fixed point method in first step and modification of the generalized Newton method introduced by Mangasarian in second step. It is proved that the proposed algorithm has all of the properties of the generalized Newton method while converges faster than it. Especially, our wide numerical experiments showed that our algorithm can solve much more problems with an accuracy of 10−11, whereas the generalized Newton method may fail.
