Continuous model and verification of G-type Zhang reciprocal (ZR) conquering 1/0 singularity of four kinds

摘要

Although the static reciprocal calculation has been studied for many centuries, the 1/0 singularity can not be conquered in the static situation. Zhang et al have investigated and solved a rich repertoire of time-varying problems such as the time-varying reciprocal problem. When we regard the reciprocal as a time-varying process, the 1/0 singularity can be conquered unexpectedly but also naturally. In this paper, we focus on the 1/0-included time-varying reciprocal (termed Zhang reciprocal, ZR) calculation, and the continuous model of G-type ZR is presented and developed for the first time to conquer the 1/0 singularity of four kinds, i.e., zero-touching kind, zero-crossing kind, zero-holding-but-not-crossing kind and zero-holding-and-crossing kind. Moreover, the efficacy of the continuous G-type ZR model for conquering 1/0 singularity of four kinds is verified evidently through simulation results.