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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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
Title of host publication	Eigenvalue Problems
Subtitle of host publication	Algorithms, Software and Applications in Petascale Computing - EPASA 2015
Editors	Yoshinobu Kuramashi, Takeo Hoshi, Tetsuya Sakurai, Toshiyuki Imamura, Shao-Liang Zhang, Yusaku Yamamoto
Publisher	Springer Verlag
Pages	143-155
Number of pages	13
ISBN (Print)	9783319624242
DOIs	https://doi.org/10.1007/978-3-319-62426-6_10
Publication status	Published - 2017
Event	1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015 - Tsukuba, Japan Duration: 2015 Sept 14 → 2015 Sept 16

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	117
ISSN (Print)	1439-7358

Other

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

Access to Document

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

Cite this

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 et al.
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).

Research output: Chapter in Book/Report/Conference proceeding › 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 et al. / 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.",

author = "Hiroshi Takeuchi and Kensuke Aihara and Akiko Fukuda and Emiko Ishiwata",

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Computation of eigenvectors for a specially structured banded matrix

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