IEICE TRANSACTIONS on Fundamentals
Performance Evaluation of Hopfield Network for Simple Examples
Summary :
The performance guarantees of the Hopfield networks are given for two simple graph problems. A lower bound of the cutsize is evaluated for the maximum cut problem through the analysis of the eigenvalues at equilibrium states. The condition of constraint satisfaction and an upper bound of the cutsize are also given for the graph bipartitioning problem. In addition an effective numerical scheme is proposed to integrate the differential equations of the Hopfield networks by using backward Euler formula with one-step Gauss-Seidel relaxation. Theoretical estimates of the performance of the algorithm are verified experimentally.
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- IEICE TRANSACTIONS on Fundamentals Vol.E74-A No.6 pp.1471-1475
- Publication Date
- 1991/06/25
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- Special Section PAPER (Special Issue on Nonlinear Theory and Its Applications)
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Kiichi URAHAMA, "Performance Evaluation of Hopfield Network for Simple Examples" in IEICE TRANSACTIONS on Fundamentals,
vol. E74-A, no. 6, pp. 1471-1475, June 1991, doi: .
Abstract: The performance guarantees of the Hopfield networks are given for two simple graph problems. A lower bound of the cutsize is evaluated for the maximum cut problem through the analysis of the eigenvalues at equilibrium states. The condition of constraint satisfaction and an upper bound of the cutsize are also given for the graph bipartitioning problem. In addition an effective numerical scheme is proposed to integrate the differential equations of the Hopfield networks by using backward Euler formula with one-step Gauss-Seidel relaxation. Theoretical estimates of the performance of the algorithm are verified experimentally.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e74-a_6_1471/_p
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@ARTICLE{e74-a_6_1471,
author={Kiichi URAHAMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Performance Evaluation of Hopfield Network for Simple Examples},
year={1991},
volume={E74-A},
number={6},
pages={1471-1475},
abstract={The performance guarantees of the Hopfield networks are given for two simple graph problems. A lower bound of the cutsize is evaluated for the maximum cut problem through the analysis of the eigenvalues at equilibrium states. The condition of constraint satisfaction and an upper bound of the cutsize are also given for the graph bipartitioning problem. In addition an effective numerical scheme is proposed to integrate the differential equations of the Hopfield networks by using backward Euler formula with one-step Gauss-Seidel relaxation. Theoretical estimates of the performance of the algorithm are verified experimentally.},
keywords={},
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ISSN={},
month={June},}
Copy
TY - JOUR
TI - Performance Evaluation of Hopfield Network for Simple Examples
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1471
EP - 1475
AU - Kiichi URAHAMA
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E74-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 1991
AB - The performance guarantees of the Hopfield networks are given for two simple graph problems. A lower bound of the cutsize is evaluated for the maximum cut problem through the analysis of the eigenvalues at equilibrium states. The condition of constraint satisfaction and an upper bound of the cutsize are also given for the graph bipartitioning problem. In addition an effective numerical scheme is proposed to integrate the differential equations of the Hopfield networks by using backward Euler formula with one-step Gauss-Seidel relaxation. Theoretical estimates of the performance of the algorithm are verified experimentally.
ER -
English
