Modified discrete iterations for computing the inverse and pseudoinverse of the time-varying matrix

The general discretization scheme for transforming continuous-time ZNN models for matrix inversion and pseudoinversion into corresponding discrete-time iterative methods is developed and investigated. The proposed discrete-time ZNN models incorporate scaled Hyperpower iterative methods as well as the Newton iteration in certain cases. The general linear Multi-step method is applied in order to obtain the proposed discretization rule which comprises all previously proposed discretization schemes. Both the Euler difference rule and the Taylor-type difference rules are included in the general scheme. In particular, the iterative scheme based on the 4th order Adams-Bashforth method is proposed and numerically compared with other known iterative schemes. In addition, the ZNN model for computing the time-varying matrix inverse is extended to the singular or rectangular case for the pseudoinverse computation. Convergence properties of the continuous-time ZNN model in the case of the Moore-Penrose inverse and its discretization are also considered.