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.

翻译：对于以线性部分系数矩阵的转移分差为基础的粗略普遍绝对值方程式(GAVE),我们建立了一个新的修改型牛顿型迭代法,深入讨论了NMN迭代法的趋同条件,此外,当系数矩阵是一个对称正数确定矩阵和一个$H+$-matrix时,可以得出一些具体的足够趋同条件。两个数字例子都表明NMN迭代法是解决GAVE的有效办法,特别是当系数矩阵是无限期的时。