Discrete-time recurrent neural network for solving discrete-form time-variant complex division

In recent years, recurrent neural network (RNN) model has been widely investigated for time-variant problems. In this paper, we focus on discrete-form time-variant complex division solving. Firstly, based on the traditional Euclid division, we present the problem formulation of time-variant complex division. Then, in the continuous-time environment, time-variant complex division is converted a simple time-variant matrix vector equation equivalently; correspondingly, discrete-form time-variant complex division is converted a discrete-form time-variant matrix vector equation. Secondly, we present different discretization formulas and corresponding different discrete-time recurrent neural network (DTRNN) models that have different accuracy for solving the discrete-form time-variant matrix vector equation. Finally, comparative numerical experimental results are conducted to prove the effectiveness of the DTRNN models for solving discrete-form time-variant complex division.