In this paper, we propose a regular smoothing approximation method to solve the NP-hard absolute value equation when the solution is unique. To this end, we regularly approximate the absolute value in such a way that the nonsmooth absolute value. equation can be fonnulated as a smooth nonlinear equation. By: solving the regular smooth nonlinear equation using Newton method, we can get the solution of the absolute value equation. We will prove that our method is well defined, bounded, and globally convergent. Numerical results indicate . effectiveness and robustness of the method to solve absolute value equations
