A noise-suppressing discrete-time neural dynamics model for solving time-dependent multi-linear [formula omitted]-tensor equation

Abstract

Neural dynamics plays an important role in handling various complex problems related to matrices or even tensors, e.g., the multi-linear M-tensor equation investigated in this paper. However, the existing methods for computing the time-dependent multi-linear M-tensor equation bear the following weaknesses: 1) all of them are under the short-time invariant hypothesis, thereby generating considerable residual errors for time-dependent ones; 2) most of them are depicted in continuous-time form, which can not be directly implemented in the digital equipment; and 3) all of them only consider the noise-free conditions, lacking robustness over truncation errors and round-off errors widely existing in the digital equipment. This paper remedies these three weaknesses by proposing a noise-suppressing discrete-time neural dynamics (NSDTND) model for the time-dependent multi-linear M-tensor equation. Additionally, analyses on the convergence and robustness are shown to demonstrate that the proposed NSDTND model is globally convergent and has a superior immunity to noises. Then, numerical experimental verifications and an application to the particle movement are provided to prove the superiority and effectiveness of the proposed NSDTND model for solving time-dependent multi-linear M-tensor equation with noises considered.