Discrete Zhang Neural Dynamics Algorithms for Time-Varying Matrix Generalized Sinkhorn Scaling

Abstract

In this paper, we first introduce a continuous model for time-varying matrix generalized Sinkhorn scaling (TVMGSS) on the basis of the continuous Zhang neural dynamics (ZND) model. Subsequently, a high-precision 10-instant Zhang time discretization (ZTD) formula with theoretical analysis is presented. Further, we utilize the 10-instant ZTD formula to discretize the continuous ZND model, resulting in a discrete ZND algorithm named 10-instant discrete ZND (10IDZND) algorithm for TVMGSS. For comparison, two other time discretization formulas are also considered, and the corresponding discrete algorithms for TVMGSS are derived. The comparative numerical experiments are performed, and the results substantiate the effectiveness and superior accuracy of the 10IDZND algorithm. In addition, we verify the effectiveness of the 10IDZND algorithm for higher-dimensional TVMGSS through numerical experiments. Finally, we experimentally investigate the effects of the design parameters and the sampling period on the convergence of the 10IDZND algorithm.