An analog scheme for fixed point computation - part i: theory

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 44, Issue 4, 1997, Pages 351-355

  Borkar, Vivek S ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; DYNAMIC PROGRAMMING; ITERATIVE METHODS;

ANALOG SYSTEM; ENERGY MINIMIZATION TECHNIQUES; FIXED POINT COMPUTATION;

SYSTEM THEORY;

EID: 0031123471     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.563625     Document Type: Article

References (23)

1. M. K. M. Au and F. Kamoun, "Neural networks for shortest path computation and routing in computer networks," IEEE Trans. Neural Networks, vol. 4, pp. 931-940, Nov. 1993.
2. B. Linares Barranco, E. Sanchez-Sinenco, A. Rodriguez-Vazquez, and J. L. Huertas, "A modular T-mode design approach for analog neural network hardware implementations," IEEE J. Solid State Circuits, vol. 27, pp. 701-713, May 1992.
3. D. Bertsekas and J. Tsitsiklis, Parallel and Distributed Computation. Englewood Cliffs, NJ: Prentice Hall, 1989.
4. V. S. Borkar, "Topics in controlled Markov chains," Pitman Research Notes in Mathematics, No 240, Longman Scientific and Technical, Harlow, England, 1991.
5. A. Bouzerdoum and T. R. Pattison, "Neural network for quadratic optimization with bound constraints," IEEE Trans. Neural Networks, vol. 4, pp. 293-304, 1993.
6. R. W. Brockett, "Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems," in Linear Algebra and its Applications, vol. 146, pp. 79-91, 1991.
7. "Least squares matching problems," Center for Intell. Contr. Syst. Rep. CICS-P-133, Harvard Univ., MA, Apr. 1989.
8. R. W. Brockett and W. S. Wong, "A gradient flow for the assignment problem," Center for Intell. Contr. Syst. Rep. CICS-P-284, Harvard Univ., MA, Feb. 1991.
9. L. O. Chua and G. N. Liu, "Nonlinear programming without computation," IEEE Trans. Circuits Syst., vol. 31, pp. 182-188, 1984.
10. L. O. Chua and L. Yang, "Cellular neural networks: Theory and applications," IEEE Trans. Circuits. Syst., vol. 35, pp. 1257-1290, 1988.
11. T. Roska and L. O. Chua "The CNN universal machine: An analogic array," IEEE Trans. Circuits Syst., vol. 40, pp. 163-173, Mar. 1993.
12. C. Chiu, C. Y. Maa, and M. A. Shanblatt, "Energy function analysis of dynamic programming neural networks," IEEE Trans. Neural Networks, vol. 2, pp. 418-426, July 1991.
13. M. T. Chu, "On the continuous realization of iterative processes," SIAM Rev., vol. 30. no. 3, Sept. 1988.
14. A. Cichocki and R. Unbehauen, "Neural networks for solving systems of linear equations - Part II: Minimax and least absolute value problems," IEEE Trans. Circuits Syst. II, vol. 39 pp. 619-633, 1991.
15. J. Cronin, Differential Equations: Introduction and Qualitative Theory. New York: Marcel Dekker, 1994, second ed.
16. C. B. Garcia and W. I. Zangwill, Pathways to Solutions, Fixed Points and Equilibria. Englewood Cliffs, NJ: Prentice-Hall, 1981.
17. D. G. Kelly, "Stability in contractive neural networks," IEEE Trans. Biomed. Eng., vol. 37, pp. 231-242, Mar. 1990.
18. M. K. Kennedy and L. O. Chua, "Neural networks for nonlinear programming," IEEE Trans. Ciruits Syst., vol. 35, pp. 554-562, 1988.
19. K. Matsuoka, "Stability conditions for nonlinear continuous neural networks with asymmetric connection weights," Neural Networks, vol. 5, pp. 495-500, 1992.
20. S. Smale, "A convergent process of price adjustment and global newton methods," J. Math. Economics, vol. 3, pp. 107-120, 1976.
21. G. R. Sell, Topological Dynamics and Ordinary Differential Equations. London, England: Van Nostrand Reinhold, 1971.
22. L. Zhang and S. C. A. Thomopoulos, "Neural network implementation of the shortest path algorithm for traffic routing in communication networks," in Proc. Int. Joint Conf. Neural Networks, June 1989, p. II 591.
23. M. Vidyasagar, Nonlinear System Analysis. Englewood Cliffs, NJ: Prentice Hall, 1992.