### Abstract

The performance guarantees of the Hopfield network are given for two simple graph problems. A lower bound of cutsize is evaluated for the maximum cut problem through the analysis of eigenvalues at equilibrium states. The condition of constraint satisfaction and an upper bound of the cutsize are given for the graph bipartitioning problem. In addition, an effective numerical scheme is proposed to integrate the differential equations of the Hopfield network by using the backward Euler formula with one-step Gauss-Seidel relaxation. Theoretical estimates of the performance of the algorithm are verified experimentally.

Original language | English |
---|---|

Pages (from-to) | 1412-1415 |

Number of pages | 4 |

Journal | Unknown Journal |

Volume | 3 |

Publication status | Published - 1991 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials

### Cite this

*Unknown Journal*,

*3*, 1412-1415.

**Performance evaluation of Hopfield network for simple examples.** / Urahama, Kiichi.

Research output: Contribution to journal › Article

*Unknown Journal*, vol. 3, pp. 1412-1415.

}

TY - JOUR

T1 - Performance evaluation of Hopfield network for simple examples

AU - Urahama, Kiichi

PY - 1991

Y1 - 1991

N2 - The performance guarantees of the Hopfield network are given for two simple graph problems. A lower bound of cutsize is evaluated for the maximum cut problem through the analysis of eigenvalues at equilibrium states. The condition of constraint satisfaction and an upper bound of the cutsize are given for the graph bipartitioning problem. In addition, an effective numerical scheme is proposed to integrate the differential equations of the Hopfield network by using the backward Euler formula with one-step Gauss-Seidel relaxation. Theoretical estimates of the performance of the algorithm are verified experimentally.

AB - The performance guarantees of the Hopfield network are given for two simple graph problems. A lower bound of cutsize is evaluated for the maximum cut problem through the analysis of eigenvalues at equilibrium states. The condition of constraint satisfaction and an upper bound of the cutsize are given for the graph bipartitioning problem. In addition, an effective numerical scheme is proposed to integrate the differential equations of the Hopfield network by using the backward Euler formula with one-step Gauss-Seidel relaxation. Theoretical estimates of the performance of the algorithm are verified experimentally.

UR - http://www.scopus.com/inward/record.url?scp=0026404664&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026404664&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0026404664

VL - 3

SP - 1412

EP - 1415

JO - Quaternary International

JF - Quaternary International

SN - 1040-6182

ER -