The generalized fixed point iteration method for AVE

Abstract:

      In this paper, based on the previous published work by Ke et al.(2019) and Li et al.(2022), by using the matrix splitting technique, generalized fixed point iteration method (GFPI) is established to solve the absolute value equation (AVE). The proposed method not only includes SOR-like method, FPI method, MFPI method and so on, but also generates some special versions. Some convergence conditions of the proposed method with different iteration error norms are presented. Furthermore, methods corresponding to other splitting methods are studied in detail. The effectiveness and feasibility of the proposed method are confirmed by some numerical experiments.