GMDS-ZNN Variants Having Errors Proportional to Sampling Gap as Compared with Models 1 and 2 Having Higher Precision

Abstract

In this paper, variants of Getz-Marsden dynamic system (GMDS) and Zhang neural network (ZNN), i.e., GMDS-ZNN variants, are proposed and discretized by different discretization formulas, i.e., discretized by Euler forward formula, Taylor-Zhang discretization formula and ZD5i (Zhang discretization with 5 instants) formula. In order to investigate the proposed GMDS-ZNN variants, we conduct numerical experiments, As comparisons, conventional dynamic systems GMDSI and GMDS2 (which are proved to have higher precision) are presented. Numerical results show that these discrete GMDS-ZNN variants have fixed error pattern when computing time-dependent complex matrix inverse. The error pattern is confirmed as being proportional to sampling gap.