An inexact Picard iteration method for absolute value equation

Recently, a class of inexact Picard iteration method for solving the absolute value equation: $Ax-|x~|=b$ have been proposed in [Optim Lett 8:2191-2202,2014]. To further improve the performance of Picard iteration method, a new inexact Picard iteration method is proposed to solve the absolute value equation. The sufficient conditions for the convergence of the proposed method for the absolute value equation is given. Some numerical experiments are given to demonstrate the effectiveness of the new method.