A shift splitting modified Newton-type (SSMN) iteration method is introduced for solving large sparse generalized absolute value equations (GAVEs). The SSMN method is established by replacing the regularized splitting of the coefficient matrix of the linear part, which is employed in the modified Newton-type (MN) iteration method, with the shift splitting of the matrix. The conditions for the convergence of the proposed method are discussed in depth for the cases when the coefficient matrix is a general matrix, a symmetric positive definite matrix, and an $H_{+}$-matrix. Through two numerical examples, we find that the SSMN and MN methods complement each other. The optimal performances of the two methods depend on the definiteness of the coefficient matrix of the linear part. The MN method is more efficient when the coefficient matrix is positive definite, whereas the SSMN method has a better performance when the coefficient matrix is indefinite.

翻译：引入了分班制修改牛顿型(SSMN)迭代法,以解决大量稀少的通用绝对值方程式(GAVES)问题。确定SSMN方法的方法是用修改的牛顿型(MN)迭代法取代线性部分系数矩阵的正规分割法,采用分流法,采用分流法。当系数矩阵是通用矩阵、对称正数确定矩阵和$H ⁇ $-美元矩阵时,将深入讨论拟议方法的趋同条件。通过两个数字示例,我们发现SSMN和MNM方法相互补充。两种方法的最佳性能取决于线性部分系数矩阵的确定性。当系数矩阵是肯定的时,MNW方法更有效率,而当系数矩阵是不确定时,SMN方法的性能更好。