### Abstract

For a specially structured nonsymmetric banded matrix, which is related to a discrete integrable system, we propose a novel method to compute all the eigenvectors. We show that the eigenvector entries are arranged radiating out from the origin on the complex plane. This property enables us to efficiently compute all the eigenvectors. Although the intended matrix has complex eigenvalues, the proposed method can compute all the complex eigenvectors using only arithmetic of real numbers.

Original language | English |
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Title of host publication | Eigenvalue Problems |

Subtitle of host publication | Algorithms, Software and Applications in Petascale Computing - EPASA 2015 |

Publisher | Springer Verlag |

Pages | 143-155 |

Number of pages | 13 |

ISBN (Print) | 9783319624242 |

DOIs | |

Publication status | Published - 2017 Jan 1 |

Event | 1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015 - Tsukuba, Japan Duration: 2015 Sep 14 → 2015 Sep 16 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 117 |

ISSN (Print) | 1439-7358 |

### Other

Other | 1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015 |
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Country | Japan |

City | Tsukuba |

Period | 15/9/14 → 15/9/16 |

### ASJC Scopus subject areas

- Modelling and Simulation
- Engineering(all)
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Mathematics

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## Cite this

Takeuchi, H., Aihara, K., Fukuda, A., & Ishiwata, E. (2017). Computation of eigenvectors for a specially structured banded matrix. In

*Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015*(pp. 143-155). (Lecture Notes in Computational Science and Engineering; Vol. 117). Springer Verlag. https://doi.org/10.1007/978-3-319-62426-6_10