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

For the large sparse generalized absolute value equations (GAVEs) , the shift splitting for the linear part's coefficient matrix is utilized to establish a new modified Newton-type (NMN) iteration method. The conditions for the convergence of the NMN iteration method are discussed in depth. Furthermore, certain sufficient convergence conditions are obtained when the coefficient matrix is a symmetric positive definite matrix or an $H_{+}$-matrix. According to both two numerical examples, the NMN iteration method is an effective approach to solve the GAVEs, especially when the coefficient matrix is indefinite.