Complex, Temporally Variant SVD via Real ZN Method and 11-Point ZeaD Formula from Theoretics to Experiments

The complex, temporally variant singular value decomposition (SVD) problem is proposed and investigated in this paper. Firstly, the original problem is transformed into an equation system. Then, by using the real zeroing neurodynamics (ZN) method, matrix vectorization, Kronecker product, vectorized transpose matrix, and dimensionality reduction technique, a dynamical model, termed the continuous-time SVD (CTSVD) model, is derived and investigated. Furthermore, a new 11-point Zhang et al. discretization (ZeaD) formula with fifth-order precision is proposed and studied. In addition, with the use of the 11-point and other ZeaD formulas, five discrete-time SVD (DTSVD) algorithms are further acquired. Meanwhile, theoretical analyses and numerical experimental results substantiate the correctness and convergence of the proposed CTSVD model and DTSVD algorithms.