Three Different Continuous-Time GMDS-ZNN Models and Multiple-Instant Discrete-Time Ones for Time-Varying Matrix Inversion with Comparisons

Securing the inverse matrix of a matrix varied with time online plays a considerable role in many engineering and scientific applications. Lots of effort has been made in securing the inverse varied with time of an interesting matrix with high speed and high accuracy so far. With the rapid development of neural networks and neural-dynamic methods, Getz-Marsden dynamic system (GMDS) is propounded to secure the time-varying matrix inversion. Subsequently, Zhang et al. put forward Zhang neural network (ZNN, also zeroing neural network as termed) models and Zhang functions (ZFs, also termed zeroing functions), with several kinds of GMDS-ZNN (GZ) models constructed in real and complex domains by means of ZNN models and ZFs. In the meantime, many researches on the features of these GZ models are carried out. However, there is no comparison among these GZ models. Hence, we conduct numerical experiments to compare three GZ models, including GZ model 1 (also termed GMDS), GZ model 2, and GZ model 3. The results of numerical computer experiments substantiate that GZ model 2 and 3 are evidently better in two aspects (i.e., convergence accuracy and convergence rate), compared with GZ model 1. Besides, the numerical results synthesized by GZ model 2 are completely the same as those synthesized by GZ model 3.