求解绝对值方程的广义不动点迭代法

The Generalized Fixed Point Iteration Method for AVE

中文关键词:  绝对值方程  不动点迭代法  收敛性

英文关键词:absolute value equations  fixed point iteration  convergence

中文摘要:

      基于Ke(2019)和Li等(2022)的工作,利用矩阵分裂技术,建立了求解绝对值方程的广义不动点迭代法(GFPI).该方法不仅包含了已有的SOR-like方法、FPI方法、MFPI方法等,而且形成了一类更广泛的迭代框架.该方法在不同迭代误差范数下的收敛条件被给出.此外,还详细研究了与其他分裂方法相对应的方法.数值实验验证了所提方法的有效性和可行性.

英文摘要:

      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.