Proposal, verification and comparison on infinitely many ZTFs leading to various nets for Zhang matrix inverse solving

Abstract

Lately, Zhang et al have proposed the notion of infinitely many Z-type functions (ZTFs) leading to various Z-type neural nets (ZTNNs), and established a systematic approach (i.e., the general-form ZTNN, GFZTNN) for the real-time solution of a time-varying matrix inverse (also termed, Zhang matrix inverse, ZMI). Being a supplementary and in-depth research, this paper provides the theoretical result on the convergence performance of the GFZTNN model. Besides, such a GFZTNN model is generalized and exploited for computing the time-varying Drazin inverse (TVDI) instead of the usual constant one. Finally, computer simulations with two illustrative examples are performed to show the efficacy and advantage of two specific ZTNN models originating from the GFZTNN model for the realtime solution of ZMI and/or TVDI.