Computation of eigenvectors for a specially structured banded matrix

Hiroshi Takeuchi; Kensuke Aihara; Akiko Fukuda; Emiko Ishiwata

doi:10.1007/978-3-319-62426-6_10

Computation of eigenvectors for a specially structured banded matrix

Hiroshi Takeuchi, Kensuke Aihara, Akiko Fukuda, Emiko Ishiwata

研究成果: Conference contribution

抄録

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.

本文言語	English
ホスト出版物のタイトル	Eigenvalue Problems
ホスト出版物のサブタイトル	Algorithms, Software and Applications in Petascale Computing - EPASA 2015
編集者	Yoshinobu Kuramashi, Takeo Hoshi, Tetsuya Sakurai, Toshiyuki Imamura, Shao-Liang Zhang, Yusaku Yamamoto
出版社	Springer Verlag
ページ	143-155
ページ数	13
ISBN（印刷版）	9783319624242
DOI	https://doi.org/10.1007/978-3-319-62426-6_10
出版ステータス	Published - 2017
イベント	1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015 - Tsukuba, Japan 継続期間: 2015 9月 14 → 2015 9月 16

出版物シリーズ

名前	Lecture Notes in Computational Science and Engineering
巻	117
ISSN（印刷版）	1439-7358

Other

Other	1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015
国/地域	Japan
City	Tsukuba
Period	15/9/14 → 15/9/16

ASJC Scopus subject areas

モデリングとシミュレーション
工学（全般）
離散数学と組合せ数学
制御と最適化
計算数学

文献へのアクセス

10.1007/978-3-319-62426-6_10

他のファイルとリンク

引用スタイル

Takeuchi, H., Aihara, K., Fukuda, A., & Ishiwata, E. (2017). Computation of eigenvectors for a specially structured banded matrix. In Y. Kuramashi, T. Hoshi, T. Sakurai, T. Imamura, S-L. Zhang, & Y. Yamamoto (Eds.), 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

Computation of eigenvectors for a specially structured banded matrix. / Takeuchi, Hiroshi; Aihara, Kensuke; Fukuda, Akiko その他.
Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. ed. / Yoshinobu Kuramashi; Takeo Hoshi; Tetsuya Sakurai; Toshiyuki Imamura; Shao-Liang Zhang; Yusaku Yamamoto. Springer Verlag, 2017. p. 143-155 (Lecture Notes in Computational Science and Engineering; Vol. 117).

研究成果: Conference contribution

Takeuchi, H, Aihara, K, Fukuda, A & Ishiwata, E 2017, Computation of eigenvectors for a specially structured banded matrix. in Y Kuramashi, T Hoshi, T Sakurai, T Imamura, S-L Zhang & Y Yamamoto (eds), Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. Lecture Notes in Computational Science and Engineering, vol. 117, Springer Verlag, pp. 143-155, 1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015, Tsukuba, Japan, 15/9/14. https://doi.org/10.1007/978-3-319-62426-6_10

Takeuchi H, Aihara K, Fukuda A, Ishiwata E. Computation of eigenvectors for a specially structured banded matrix. In Kuramashi Y, Hoshi T, Sakurai T, Imamura T, Zhang S-L, Yamamoto Y, editors, Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. Springer Verlag. 2017. p. 143-155. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-62426-6_10

Takeuchi, Hiroshi ; Aihara, Kensuke ; Fukuda, Akiko その他. / Computation of eigenvectors for a specially structured banded matrix. Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. editor / Yoshinobu Kuramashi ; Takeo Hoshi ; Tetsuya Sakurai ; Toshiyuki Imamura ; Shao-Liang Zhang ; Yusaku Yamamoto. Springer Verlag, 2017. pp. 143-155 (Lecture Notes in Computational Science and Engineering).

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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.",

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Computation of eigenvectors for a specially structured banded matrix

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出版物シリーズ

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ASJC Scopus subject areas

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