Time-varying square roots finding via Zhang dynamics versus gradient dynamics and the former's link and new explanation to Newton-Raphson iteration

Information Processing Letters

Volumn 110, Issue 24, 2010, Pages 1103-1109

  Zhang, Yunong ^a   Ke, Zhende ^a   Xu, Peng ^a   Yi, Chenfu ^a  

^a SUN YAT SEN UNIVERSITY   (China)

Author keywords

Gradient dynamics; Indefinite error function; Newton Raphson iteration; Parallel algorithms; Real time systems; Square roots finding; Zhang dynamics

Indexed keywords

GRADIENT DYNAMICS; INDEFINITE ERROR-FUNCTION; NEWTON RAPHSON ITERATION; SQUARE ROOTS; ZHANG DYNAMICS;

COMPUTER SIMULATION; CONTINUOUS TIME SYSTEMS; DYNAMICS; HOPFIELD NEURAL NETWORKS; ITERATIVE METHODS; NEURAL NETWORKS; NONLINEAR EQUATIONS; PARALLEL ALGORITHMS; PARALLEL ARCHITECTURES; PROBLEM SOLVING; TIME VARYING SYSTEMS;

REAL TIME SYSTEMS;

EID: 77957605920     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ipl.2010.09.013     Document Type: Article

References (27)

1. J.H. Mathews, and K.D. Fink Numerical Methods Using MATLAB 2005 Publishing House of Electronics Industry Beijing, BJ, CHN
2. C. Lin Numerical Computation Methods 2005 Science Press Beijing, BJ, CHN
3. J. Feng, G. Che, and Y. Nie Principles of Numerical Analysis 2001 Science Press Beijing, BJ, CHN
4. N.J. Higham Stable iterations for the matrix square root Numerical Algorithms 15 2 1997 227 242
5. D. Takahashi, Implementation of multiple-precision parallel division and square root on distributed-memory parallel computers, in: Proceedings of the Parallel Processing, 2000, pp. 229-235.
6. F. Kong, Z. Cai, J. Yu, and D.X. Li Improved generalized Atkin algorithm for computing square roots in finite fields Information Processing Letters 98 1 2006 1 5
7. S. Abbasbandy Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method Applied Mathematics and Computation 145 2-3 2003 887 893
8. J.B. Qian, and C.A. Wang How much precision is needed to compare two sums of square roots of integers Information Processing Letters 100 5 2006 194 198
9. M. Basto, V. Semiao, and F.L. Calheiros A new iterative method to compute nonlinear equations Applied Mathematics and Computation 173 1 2006 468 483
10. Y. Zhang, W.E. Leithead, D.J. Leith, Time-series Gaussian process regression based on Toeplitz computation of O (N 2 ) operations and O(N)-level storage, in: Proceedings of the 44th IEEE Conference on Decision and Control, 2005, pp. 3711-3716.
11. C. Mead Analog VLSI and Neural Systems 1989 Addison-Wesley Reading, MA, USA
12. Y. Zhang, W. Ma, K. Li, and C. Yi Brief history and prospect of coprocessors China Academic Journal Electronic Publishing House 13 2008 115 117
13. Y. Zhang, C. Yi, D. Guo, J. Zheng, Comparison on Zhang neural dynamics and gradient-based neural dynamics for online solution of nonlinear time-varying equation, Neural Computing and Applications, in press, doi: 10.1007/s00521-010-0452-y.
14. Y. Zhang, C. Yi, and W. Ma Comparison on gradient-based neural dynamics and Zhang neural dynamics for online solution of nonlinear equations Lecture Notes in Computer Science vol. 5370 2008 269 279
15. Y. Zhang, and Z. Li Zhang neural network for online solution of time-varying convex quadratic program subject to time-varying linear-equality constraints Physics Letters A 373 18-19 2009 1639 1643
16. Y. Zhang, W. Ma, and B. Cai From Zhang neural network to Newton iteration for matrix inversion IEEE Transactions on Circuits and Systems 56 7 2009 1405 1415
17. The MathWorks Inc., Simulink 7 Getting Started Guide, Natick, MA, 2008.
18. Y. Zhang, Revisit the analog computer and gradient-based neural system for matrix inversion, in: Proceedings of the IEEE International Symposium on Intelligent Control, 2005, pp. 1411-1416.
19. Y. Zhang, P. Xu, N. Tan, Solution of nonlinear equations by continuous- and discrete-time Zhang dynamics and more importantly their links to Newton iteration, in: Proceedings of the IEEE International Conference Information, Communications and Signal Processing, 2009, pp. 1-5.
20. Y. Zhang, Towards piecewise-linear primal neural networks for optimization and redundant robotics, in: Proceedings of the IEEE International Conference on Networking, Sensing and Control, 2006, pp. 374-379.
21. Y. Zhang, D. Jiang, and J. Wang A recurrent neural network for solving Sylvester equation with time-varying coefficients IEEE Transactions on Neural Networks 13 5 2002 1053 1063
22. Y. Zhang, and S.S. Ge Design and analysis of a general recurrent neural network model for time-varying matrix inversion IEEE Transactions on Neural Networks 16 6 2005 1477 1490
23. Y. Zhang A set of nonlinear equations and inequalities arising in robotics and its online solution via a primal neural network Neurocomputing 70 2006 513 524
24. Y. Zhang, Y. Yang, Simulation and comparison of Zhang neural network and gradient neural network solving for time-varying matrix square roots, in: Proceedings of the 2nd International Symposium on Intelligent Information Technology Application, 2008, pp. 966-970.
25. Y. Zhang, H. Peng, Zhang neural network for linear time-varying equation solving and its robotic application, in: Proceedings of the 6th International Conference on Machine Learning and Cybernetics, 2007, pp. 3543-3548.
26. Y. Zhang, Z. Chen, K. Chen, B. Cai, Zhang neural network without using time-derivative information for constant and time-varying matrix inversion, in: Proceedings of the International Joint Conference on Neural Networks, 2008, pp. 142-146.
27. S.K. Mitra Digital Signal Processing-A Computer-Based Approach 3rd ed. 2006 Tsinghua University Press Beijing, BJ, CHN