A generalization of the Newton-based matrix splitting iteration method (GNMS) for solving the generalized absolute value equations (GAVEs) is proposed. Under mild conditions, the GNMS method converges to the unique solution of the GAVEs. Moreover, we can obtain a few weaker convergence conditions for some existing methods. Numerical results verify the effectiveness of the proposed method.

翻译：提出了一种广义绝对值方程(GAVEs)的基于牛顿的矩阵分裂迭代法(GNMS)的推广形式。在温和条件下，GNMS方法收敛于GAVEs的唯一解。此外，我们还能为某些现有方法推导出几个更弱的收敛条件。数值结果验证了所提方法的有效性。