Analog VLSI and neural systems
Analog VLSI and neural systems
Numerical Methods Using MATLAB
Numerical Methods Using MATLAB
ICPP '00 Proceedings of the 2000 International Workshop on Parallel Processing
Digital Signal Processing
How much precision is needed to compare two sums of square roots of integers?
Information Processing Letters
IITA '08 Proceedings of the 2008 Second International Symposium on Intelligent Information Technology Application - Volume 02
ISICA '08 Proceedings of the 3rd International Symposium on Advances in Computation and Intelligence
From Zhang neural network to Newton iteration for matrix inversion
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Improved generalized Atkin algorithm for computing square roots in finite fields
Information Processing Letters
ICICS'09 Proceedings of the 7th international conference on Information, communications and signal processing
Neural Computing and Applications
A recurrent neural network for solving Sylvester equation with time-varying coefficients
IEEE Transactions on Neural Networks
Design and analysis of a general recurrent neural network model for time-varying matrix inversion
IEEE Transactions on Neural Networks
Improved gradient-based neural networks for online solution of Lyapunov matrix equation
Information Processing Letters
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part I
ISNN'13 Proceedings of the 10th international conference on Advances in Neural Networks - Volume Part II
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Different from conventional gradient-based neural dynamics, a special class of neural dynamics have been proposed by Zhang et al. since 12 March 2001 for online solution of time-varying and static (or termed, time-invariant) problems (e.g., nonlinear equations). The design of Zhang dynamics (ZD) is based on the elimination of an indefinite error-function, instead of the elimination of a square-based positive or at least lower-bounded energy-function usually associated with gradient dynamics (GD) and/or Hopfield-type neural networks. In this paper, we generalize, develop, investigate and compare the continuous-time ZD (CTZD) and GD models for online solution of time-varying and static square roots. In addition, a simplified continuous-time ZD (S-CTZD) and discrete-time ZD (DTZD) models are generated for static scalar-valued square roots finding. In terms of such scalar square roots finding problem, the Newton iteration (also termed, Newton-Raphson iteration) is found to be a special case of the DTZD models (by focusing on the static-problem solving, utilizing the linear activation function and fixing the step-size to be 1). Computer-simulation results via a power-sigmoid activation function further demonstrate the efficacy of the ZD solvers for online scalar (time-varying and static) square roots finding, in addition to the DTZD's link and new explanation to Newton-Raphson iteration.