Two common methods for solving absolute value equations (AVE) are SOR-like iteration method and fixed point iteration (FPI) method. In this paper, novel convergence analysis, which result wider convergence range, of the SOR-like iteration and the FPI are given. Based on the new analysis, a new optimal iterative parameter with a analytical form is obtained for the SOR-like iteration. In addition, an optimal iterative parameter with a analytical form is also obtained for FPI. Surprisingly, the SOR-like iteration and the FPI are the same whenever they are equipped with our optimal iterative parameters. As a by product, we give two new constructive proof for a well known sufficient condition such that AVE has a unique solution for any right hand side. Numerical results demonstrate our claims.

翻译：求解绝对值方程(AVE)的两种常用方法是类SOR迭代法和不动点迭代(FPI)法。本文对类SOR迭代和FPI给出了新颖的收敛性分析，该分析得到了更广的收敛范围。基于新分析，我们为类SOR迭代获得了一个具有解析形式的最优迭代参数。此外，也为FPI获得了一个具有解析形式的最优迭代参数。令人惊讶的是，当类SOR迭代与FPI配备我们的最优迭代参数时，两者完全相同。作为副产品，我们为一个著名的充分条件（该条件保证AVE对任意右端项具有唯一解）提供了两个新的构造性证明。数值结果验证了我们的论断。