# The neural network models with delays for solving absolute value equations

arXiv: https://arxiv.org/abs/2310.10965 · HTML: https://mlsanity.com/paper/2310.10965/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 40 references that are in the map.
- First posted on arXiv 17 Oct 2023.

## Builds on (most cited first, 2 of 2)

- [A fixed-time inverse-free dynamical system for solving the system of absolute value equations](https://mlsanity.com/paper/2208.10691/) (2022)
- [Properties of the solution set of absolute value equations and the related matrix classes](https://mlsanity.com/paper/2209.06457/) (2022)

## Abstract (arXiv)

An inverse-free neural network model with mixed delays is proposed for solving the absolute value equation (AVE) Ax -|x| - b =0, which includes an inverse-free neural network model with discrete delay as a special case. By using the Lyapunov-Krasovskii theory and the linear matrix inequality (LMI) method, the developed neural network models are proved to be exponentially convergent to the solution of the AVE. Compared with the existing neural network models for solving the AVE, the proposed models feature the ability of solving a class of AVE with |A-1|>1. Numerical simulations are given to show the effectiveness of the two delayed neural network models.