### Abstract

systems are related to matrix eigenvalue computation. Especially, we next clarify the existence of a center manifold for the discrete hungry Lotka-Volterra (dhLV) system. By using the center manifold theory, we prove that the solution of the dhLV system, employed in the dhLV algorithm for computing eigenvalues, exponentially converges to its equilibrium point.

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

Pages (from-to) | 1-17 |

Journal | RIMS kokyuroku Bessatsu |

Volume | B13 |

Publication status | Published - 2009 |

### Cite this

*RIMS kokyuroku Bessatsu*,

*B13*, 1-17.

**Discrete hungry integrable systems related to matrix eigenvalue and their local analysis by center manifold theory.** / Fukuda, Akiko; Ishiwata, Emiko; Iwasaki, Masashi; Nakamura, Yoshimasa.

Research output: Contribution to journal › Article

*RIMS kokyuroku Bessatsu*, vol. B13, pp. 1-17.

}

TY - JOUR

T1 - Discrete hungry integrable systems related to matrix eigenvalue and their local analysis by center manifold theory

AU - Fukuda, Akiko

AU - Ishiwata, Emiko

AU - Iwasaki, Masashi

AU - Nakamura, Yoshimasa

PY - 2009

Y1 - 2009

N2 - In this paper, we first review the results of [8, 9] that two discrete hungry integrablesystems are related to matrix eigenvalue computation. Especially, we next clarify the existence of a center manifold for the discrete hungry Lotka-Volterra (dhLV) system. By using the center manifold theory, we prove that the solution of the dhLV system, employed in the dhLV algorithm for computing eigenvalues, exponentially converges to its equilibrium point.

AB - In this paper, we first review the results of [8, 9] that two discrete hungry integrablesystems are related to matrix eigenvalue computation. Especially, we next clarify the existence of a center manifold for the discrete hungry Lotka-Volterra (dhLV) system. By using the center manifold theory, we prove that the solution of the dhLV system, employed in the dhLV algorithm for computing eigenvalues, exponentially converges to its equilibrium point.

M3 - Article

VL - B13

SP - 1

EP - 17

JO - RIMS kokyuroku Bessatsu

JF - RIMS kokyuroku Bessatsu

ER -