A modified inverse-free dynamical system for absolute value equations

Abstract

This paper proposes a novel inverse-free dynamical system for tackling absolute value equations. The proposed dynamical system is an extension of the inverse-free dynamical system designed by Chen et al. (Appl. Numer. Math. 168 (2021), 170-181). A new global error bound for absolute value equation is obtained, which is more compact than the existing ones. The equilibrium point of the proposed dynamical system is proved to be the solution to the corresponding absolute value equation. In contrast to some existing dynamical systems, the distinctive feature of our dynamical system is its simple structure, inverse-free operation, and global sublinear and exponential convergence. Finally, numerical results are provided to demonstrate the effectiveness of our dynamical system.