Continuous ZND (Zhang Neural Dynamics) Model for Generalized Sinkhorn Scaling of Time-Varying Matrix

Abstract

In this paper, we first propose a Zhang neural dynamics (ZND) model for the generalized Sinkhorn scaling of time-varying matrix. Specifically, by using the dimensional reduction technique, a continuous-time ZND model of time-varying matrix scaling is proposed and analyzed. In addition, the corresponding theoretical proofs are given, which prove the theoretical validity of the proposed ZND model. Moreover, two numerical experiments containing a square case and a rectangle case are also conducted. Numerical experiments and results substantiate the effectiveness and accuracy of the proposed ZND model.