An inverse-free dynamical system for solving the absolute value equations

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. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

This paper proposes an inverse-free dynamical system to solve absolute value equations, which exhibits globally asymptotically stable equilibrium points and provides a global projection-type error bound. Compared with existing dynamical systems, this method is more effective and is not limited by the eigenvalue of the coefficient matrix being 1.