A new ZNN model for finding discrete time-variant matrix square root: From model design to parameter analysis

Abstract

In recent years, artificial neural network technology has developed very rapidly. More and more experts and scholars use neural network technology to solve the related problems of applied mathematics. As a representative of the Hopfield neural network, zeroing neural network (ZNN) which can deal with the time-variant problem that may not be solved by traditional methods effectively. In this paper, to solve the problem of time-variant matrix square root, the continuous-time ZNN (CT-ZNN) model is presented based on the ZNN design formula. Next, to meet the requirements of computer simulation, the general square-pattern discretization (SPD) formula is applied to obtain the general discrete-time ZNN (G-DT-ZNN) model. Moreover, by changing the value of the selected parameter in the G-DT-ZNN model, it is presented that the effect of different values of the selected parameter on the precision of the G-DT-ZNN model. Finally, in the numerical experiments, three discrete time-variant matrix square root problems are presented as examples for verifying such theoretical results of the proposed G-DT-ZNN model.