In this paper, we propose a modified generalized SOR-like (MGSOR) method for solving an absolute value equation (AVE), which is obtained by reformulating equivalently AVE as a two-by-two block nonlinear equation and by introducing the transformation $Py:=|x|$ with a general nonsingular matrix P. The convergence results of the MGSOR method are obtained under certain assumptions imposed on the involved parameters. Furthermore, the optimal parameters minimizing the convergence rate of the MGSOR method for solving AVE are studied in detail. Numerical experiments further illustrate that the MGSOR method is efficient and has better performance than some existing iteration methods in aspects of the number of iteration steps and CPU time.

在本文中，我们提出了一种用于求解绝对值方程 (AVE) 的改进广义类 SOR (MGSOR) 方法，该方法是通过将 AVE 等价地重新表述为二乘二块非线性方程并通过引入变换获得的$P是:=|X|$具有一般非奇异矩阵P。MGSOR 方法的收敛结果是在对所涉及的参数施加某些假设的情况下获得的。此外，详细研究了最小化MGSOR方法求解AVE的收敛速度的最优参数。数值实验进一步说明MGSOR方法是高效的，在迭代步数和CPU时间方面比现有的一些迭代方法有更好的性能。