In this paper, an iterative method was considered for solving the absolute value equation (AVE). We suggest a two-step in which well-known Gauss quadrature rule is corrector step and generalized Newton taken as predictor step. The convergence of proposed established under some acceptable conditions. Numerical examples prove consistency capability new method.

We present a modified Picard-like method to solve absolute value equations by equivalently expressing the implicit fixed-point equation form of as two-by-two block nonlinear equation. This unifies some existing matrix splitting algorithms and improves efficiency algorithm introducing parameter ω. For choice ω in new method, we give way determine quasi-optimal values. Numerical examples are give...