Different types of three-step DTZD algorithms for time-varying inverse square root finding

On the basis of different error functions, a series of continuous-time Zhang dynamics (CTZD) models have been studied for time-varying inverse square root finding. For potential hardware implementation, the discrete-time forms of these CTZD models are further investigated. That is, by utilizing the Taylor-type difference rule to discretize the CTZD models, this paper proposes the corresponding discrete-time ZD (DTZD) algorithms to find time-varying inverse square root. Being a three-step iteration, each of the proposed DTZD algorithms is called the three-step DTZD algorithm in this paper. Theoretical results are also presented to highlight the computational properties of these three-step algorithms. With two illustrative examples, numerical results further demonstrate the effectiveness of the proposed algorithms in solving for time-varying inverse square root.