Simulations and Experiments of Time-Varying Takagi Factorization via Zhang Neural Network

The problem of Takagi factorization (TF) for complex time-varying symmetric matrix is proposed in this paper. To solve this difficult and challenging problem, a continuous-time TF (CTTF) model of derivative equation system form is proposed via Zhang neural network (ZNN) method. For the sake of digital hardware implementation, we also build up the corresponding discrete-time (DT) ZNN solution models with different precisions of the derivative equation system discretization. Specifically, an eight-instant DTTF (EIDTTF) model are proposed. We also comparatively use two other multi-instant (e.g., four-instant and six-instant, i.e., FIDTTF and SIDTTF, respectively) models by discretizing the CTTF model. The effective solution step-size intervals of the proposed DTTF models are further discussed lastly. The results of simulations and experiments substantiate the correctness, effectiveness and superiority of the proposed CTTF and DTTF models.