In this paper, an inverse-free dynamical system is built to solve the absolute value equations (AVEs), whose equilibrium points coincide with the solutions of the AVEs. Under proper assumptions, the equilibrium points of the dynamical system exist and could be (globally) asymptotically stable. In addition, with strongly monotone property, a global projection-type error bound is provided to estimate the distance between any trajectories and the unique equilibrium point. Compared with four existing dynamical systems for solving the AVEs, our method is inverse-free and is still valid even if 1 is an eigenvalue of the coefficient matrix. Some numerical simulations are given to show the effectiveness of the proposed method.

在本文中，建立了一个无逆动力系统来求解绝对值方程（AVE），其平衡点与 AVE 的解重合。在适当的假设下，动力系统的平衡点存在并且可以（全局）渐近稳定。此外，由于具有强单调性，提供了全局投影类型的误差界限来估计任何轨迹与唯一平衡点之间的距离。与求解 AVE 的四个现有动力学系统相比，我们的方法是无逆的，即使系数矩阵的特征值 1 仍然有效。给出了一些数值模拟来证明所提出方法的有效性。