Abstract
In this paper, the problem of online singular value decomposition (SVD) for time-varying matrix is proposed, analyzed and investigated. In order to solve this complex and difficult problem in real time, we consider to transform it into an equation system firstly. Then, by applying zeroing neural dynamics (ZND) method and a dimensional reduction technique, a continuous-time SVD (CTSVD) model is proposed. Besides, a high-precision eight-instant Zhang et al discretization (ZeaD) formula with theoretical analysis is proposed and studied. Furthermore, by using this new ZeaD formula to discretize the CTSVD model, an eight-instant discrete-time SVD (EIDTSVD) model is thus proposed. Moreover, three other discrete-time SVD (DTSVD) models termed Euler-type DTSVD (ETDTSVD) model, four-instant DTSVD (FIDTSVD) model and six-instant DTSVD (SIDTSVD) model are derived and proposed, respectively, for the purpose of comparison. Finally, numerical experiments and results further substantiate the great effectiveness, accuracy and superiority of the proposed CTSVD and EIDTSVD models.
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