In this paper, based on the previous published work by Wang et al. [Modified Newton-type iteration methods for generalized absolute value equations, Wang et al. (2019), by using the matrix splitting technique, Newton-based matrix splitting iterative method is established to solve the generalized absolute value equation. The proposed method not only covers the above modified Newton-type iterative method, but also generates some relaxation versions. Some convergence conditions of the proposed method with some special coefficient matrices are presented. The effectiveness and feasibility of the proposed method are confirmed by some numerical experiments.

中文翻译：

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广义绝对值方程的基于牛顿矩阵分解方法

在本文中，基于Wang等人先前已发表的工作。[用于广义绝对值方程的改进的牛顿型迭代方法，Wang等。（2019），通过使用矩阵分裂技术，建立了基于牛顿的矩阵分裂迭代方法来求解广义绝对值方程。所提出的方法不仅涵盖了上述改进的牛顿型迭代方法，而且还生成了一些松弛形式。给出了带有特殊系数矩阵的方法的收敛条件。数值实验证实了该方法的有效性和可行性。