A New Modified Newton-Type Iteration Methods for Solving Generalized Absolute Value Equations

For the large sparse generalized absolute value equation (GAVE), based on the shift splitting for the coefficient matrix of linear part, we establish a new modified Newton-type (NMN) iteration method. The convergence conditions of the NMN iteration method are discussed in depth. Furthermore, some specific sufficient convergence conditions are derived when the coefficient matrix is a symmetric positive definite matrix and an $H_{+}$-matrix. Both two numerical examples indicate that the NMN iteration method is an effective approach to solve the GAVE, especially when the coefficient matrix is indefinite.