An inverse-free fixed-time stable dynamical system and its forward-Euler discretization for solving generalized absolute value equations

TL;DR

This paper introduces an inverse-free dynamical system with fixed-time convergence for solving GAVE, along with a forward-Euler discretization method that guarantees finite-step convergence to the solution's neighborhood.

Contribution

It presents a novel inverse-free dynamical system with fixed-time convergence and a discretization method ensuring finite-step solution approximation for GAVE.

Findings

The proposed dynamical system converges in fixed time for all initial conditions.

The discretized iterative method guarantees convergence within a finite number of steps.

Numerical results confirm the effectiveness of the proposed methods.

Abstract

An inverse-free dynamical system is proposed to solve the generalized absolute value equation (GAVE) with a fixed time convergence, where the time of convergence is finite and is uniformly bounded for all initial points. Moreover, an iterative method obtained by using the forward-Euler discretization of the proposed dynamic model is developed and sufficient conditions which guarantee that the discrete iteration globally converge to an arbitrarily small neighborhood of the unique solution of GAVE within a finite number of iterative steps are given. Numerical results illustrate the effectiveness of the proposed methods.