Comparison on gradient-based neural dynamics and zhang neural dynamics for online solution of nonlinear equations

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5370 LNCS, Issue , 2008, Pages 269-279

  Zhang, Yunong ^a   Yi, Chenfu ^a   Ma, Weimu ^a  

^a SUN YAT SEN UNIVERSITY   (China)

Author keywords

Activation functions; Exponential convergence; Neural dynamics; Nonlinear equations; Recurrent neural networks

Indexed keywords

ACTIVATION ANALYSIS; DYNAMICS; ELECTRIC NETWORK ANALYSIS; FUNCTIONS; NEURAL NETWORKS; ORDINARY DIFFERENTIAL EQUATIONS; PROBABILITY DENSITY FUNCTION; RECURRENT NEURAL NETWORKS;

ACTIVATION FUNCTIONS; DESIGN METHODS; EXPONENTIAL CONVERGENCE; NEURAL DYNAMICS; SIMULATION RESULTS;

NONLINEAR EQUATIONS;

EID: 58549088365     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-92137-0_30     Document Type: Conference Paper

References (20)

1. Yang, L., Zhu, Z., Wang, Y.: Exact Solutions of Nonlinear Equations. Physics Letters A 260, 55-59 (1999)
2. Babolian, E., Biazar, J.: Solution of Nonlinear Equations by Modified Adomian Decomposition Method. Applied Mathematics and Computation 132, 167-172 (2002)
3. Babolian, E., Biazar, J., Vahidi, A.R.: Solution of a System of Nonlinear Equations by Adomian Decomposition Method. Applied Mathematics and Computation 150, 847-854 (2004)
4. 2) Operations and O(N)-level Storage. In: Proceedings of IEEE Conference on Decision and Control, pp. 3711-3716 (2005)
5. Jang, J., Lee, S., Shin, S.: An Optimization Network for Matrix inversion. In: Anderson, D.Z. (ed.) Neural information Processing Systems, pp. 397-401. American Institute of Physics, New York (1998)
6. Wang, J.: A Recurrent Neural Network for Real-Time Matrix inversion. Applied Mathematics and Computation 55, 89-100 (1993)
7. Zhang, Y.: Revisit the Analog Computer and Gradient-Based Neural System for Matrix inversion. In: Proceedings of IEEE International Symposium on Intelligent Control, pp. 1411-1416 (2005)
8. Zhang, Y.: Towards Piecewise-Linear Primal Neural Networks for Optimization and Redundant Robotics. In: Proceedings of IEEE International Conference on Networking, Sensing and Control, pp. 374-379 (2006)
9. Zhang, Y., Jiang, D., Wang, J.: A Recurrent Neural Network for Solving Sylvester-Equation with Time-Varying Coefficients. IEEE Transactions on Neural Networks 13, 1053-1063 (2002)
10. Zhang, Y., Ge, S.S.: Design and Analysis of a General Recurrent Neural Network Model for Time-Varying Matrix inversion. IEEE Transactions on Neural Networks 16, 1477-1490 (2005)
11. Zhang, Y., Wang, J.: Global Exponential Stability of Recurrent Neural Networks for Synthesizing Linear Feedback Control Systems via Pole Assignment. IEEE Transactions on Neural Networks 13, 633-644 (2002)
12. Zhang, Y., Wang, J.: A Dual Neural Network for Convex Quadratic Programming Subject to Linear Equality and Inequality Constraints. Physics Letters A 298, 271-278 (2002)
13. Zhang, Y.: A Set of Nonlinear Equations and Inequalities Arising in Robotics and its Online Solution via a Primal Neural Network. Neurocomputing 70, 513-524 (2006)
14. Steriti, R.J., Fiddy, M.A.: Regularized Image Reconstruction Using SVD and a Neural Network Method for Matrix Inversion. IEEE Transactions on Signal Processing 41, 3074-3077 (1993)
15. Tank, D., Hopfield, J.: Simple Neural Optimization Networks: an A/D Converter, Signal Decision Circuit, and a Linear Programming Circuit. IEEE Transactions on Circuits and Systems 33, 533-541 (1986)
16. Cichocki, A., Unbehauen, R.: Neural Network for Solving Systems of Linear Equations and Related Problems. IEEE Transactions on Circuits and Systems 39, 124-138 (1992)
17. Cichocki, A., Unbehauen, R.: Neural Networks for Optimization and Signal Processing, Wiley, Chichester (1993)
18. Manherz, R.K., Jordan, B.W., Hakimi, S.L.: Analog Methods for Computation ol the Generalized Inverse. IEEE Transactions on Automatic Control 13, 582-585 (1968)
19. Mathews, J.H., Fink, K.D.: Numerical Methods Using MATLAB, 4th edn. Pretice Hall, New Jersey (2004)
20. Zhang, Y.: Dual Neural Networks: Design, Analysis, and Application to Redundant Robotics. In: Kang, G.B. (ed.) Progress in Neurocomputing Research, pp. 41-81. Nova Science Publishers, New York (2007)