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

A generalization of the relaxation-based matrix splitting iterative method for solving the system of generalized absolute value equations