By incorporating a new matrix splitting and the momentum acceleration into the relaxed-based matrix splitting (RMS) method \cite{soso2023}, a generalization of the RMS (GRMS) iterative method for solving the generalized absolute value equations (GAVEs) is proposed. Unlike some existing methods, by using the Cauchy's convergence principle, we give some sufficient conditions for the existence and uniqueness of the solution to the GAVEs and prove that our method can converge to the unique solution of the GAVEs. Moreover, we can obtain a few new and weaker convergence conditions for some existing methods. Preliminary numerical experiments show that the proposed method is efficient.

翻译：通过引入新的矩阵分裂和动量加速技术到基于松弛的矩阵分裂方法中，提出了一种用于求解广义绝对值方程系统的推广型RMS迭代方法。与现有方法不同，我们利用柯西收敛原理，给出了广义绝对值方程组解的存在唯一性的若干充分条件，并证明了所提方法能够收敛至该唯一解。此外，我们还能为部分现有方法得到一些新的且更弱的收敛条件。初步数值实验表明，所提方法是有效的。