A uniform approximation method to solve absolute value equation

In this paper, we propose a parametric uniform approximation method to solve NP-hard absolute value equations. For this, we uniformly approximate absolute value in such a way that the nonsmooth absolute value equation can be formulated as a smooth nonlinear equation. By solving the parametric smooth nonlinear equation using Newton method, for a decreasing sequence of parameters, we can get the solution of absolute value equation. It is proved that the method is globally convergent under some weaker conditions with respect to existing methods. Moreover, preliminary numerical results indicate effectiveness and robustness of our method to solve absolute value equations.