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 equation‎. ‎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 equation‎.