Modified Newton integration neural algorithm for solving the multi-linear [formula omitted]-tensor equation

Abstract

This paper attends to solve the multi-linear equations with special structure, e.g., the multi-linear M-tensor equation, which frequently appears in engineering applications such as deep learning and hypergraph. For its critical and promising role, there are numbers of resolving schemes devoting to obtain a high-performing solution of the multi-linear M-tensor equation. However, few investigations are discovered with noise-suppression ability till now. To be proper with digital devices and further improve the solving effectiveness, it is desirable to design a discrete-time computational algorithm with noise-suppression ability and high-performing property. Inspired by the aforementioned requirements, this paper proposes a modified Newton integration (MNI) neural algorithm for solving the multi-linear M-tensor equation with noise-suppression ability. Additionally, the corresponding robustness analyses on the proposed MNI neural algorithm are provided. Simultaneously, computer simulative experiments are generated to explain the capabilities and availabilities of the MNI neural algorithm in noise suppression. As a result, in terms of noise suppression, the proposed MNI neural algorithm is superior to other related algorithms, such as Newton–Raphson iterative (NRI) algorithm (Ding and Wei, 2016), discrete time neural network (DTNN) algorithm (Wang et al., 2019), and sufficient descent nonlinear conjugate gradient (SDNCG) algorithm (Liu et al., 2020).