Forms and Results of Zhang Neuronet of Reciprocal Kind Dealing with Time-Variant Overdetermined System of Linear Equations

In order to deal with time-variant overdetermined system of linear equations (TVOSLE), a new approach termed Zhang neuronet of reciprocal kind (ZNRK) is proposed and reformulated. As developed from the continuous-time Zhang neuronet (CTZN), the ZNRK model is, however, quite different from existing CTZN models. That is, a conventional CTZN model needs to compute the inverse of the coefficient matrix. When the dimension of the coefficient matrix is large, the inverse of the coefficient matrix is difficult to compute. Hence, we propose the ZNRK model that does not need to compute the inverse of the coefficient matrix, only needing to compute the reciprocal of a scalar, which greatly reduces the computation complexity. In this paper, three computer simulations are used to test the validity of the ZNRK model, and the results substantiate the effectiveness of the ZNRK model for dealing with TVOSLE. Investigating the convergence-rate effect of the ZNRK model, we find that the convergence time decreases with the value of the convergence parameter increasing.