More than Newton iterations generalized from Zhang neural network for constant matrix inversion aided with line-search algorithm

Since 12 March 2001, Zhang et al have proposed a special class of recurrent neural networks for online time-varying problems solving, especially for matrix inversion. For possible hardware (e.g., digital-circuit) realization, such Zhang neural networks (ZNN) could also be reformulated in the discrete-time form, which incorporates Newton iteration as a special case. In this paper, for constant matrix inversion, we generalize and investigate more discrete-time ZNN models (which could also be termed as ZNN iterations) by using multiple-point backward-difference formulas. For fast convergence to the theoretical inverse, a line-search algorithm is employed to obtain an appropriate step-size value (in each iteration). Computer-simulation results demonstrate the efficacy of the presented new discrete-time ZNN models aided with a line-search algorithm, as compared to Newton iteration.