From Euclid division of constant integers to Zhang division of time-varying variables

Abstract

Static Euclid division has been studied for many decades. In this paper, we focus on time-varying division (or termed, Zhang division). As Zhang dynamics (ZD) and gradient dynamics (GD) have shown powerful abilities to solve a great variety of time-varying problems, we present a ZD model and a GD model for time-varying division by defining a Zhang function and an energy function, respectively. Through illustrative examples, the efficacy of the presented ZD and GD models for online solution of time-varying division is substantiated effectively. In addition, division-by-zero (DBZ) problem is solved readily in this paper, which is well understood.