Design and verification of different DTZD algorithms for time-varying square root finding

Recently, based on different error functions, a series of continuous-time Zhang dynamics (CTZD) models have been developed by Zhang et al to solve for time-varying square root. For completeness and also for potential digital hardware implementation, this paper further investigates the discrete-time forms of these CTZD models, which are termed as the discrete-time ZD (DTZD) algorithms. Specifically, in this paper, by utilizing the Taylor-type difference rule, different DTZD algorithms are proposed for time-varying square root finding. Then, theoretical results are provided to show the computational properties of these DTZD algorithms. Numerical results with two illustrative examples are presented to further substantiate the effectiveness of the proposed DTZD algorithms on finding time-varying square root.