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

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. On the one hand, 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 GAVEs and prove that our method can converge to the unique solution of GAVEs. On the other hand, we obtain a few new and weaker convergence conditions for some existing methods. Moreover, we establish comparison theorems between GRMS method and some existing methods. Preliminary numerical experiments show that the proposed method is efficient.