Computation of eigenvectors for a specially structured banded matrix

Hiroshi Takeuchi, Kensuke Aihara, Akiko Fukuda, Emiko Ishiwata

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationEigenvalue Problems
Subtitle of host publicationAlgorithms, Software and Applications in Petascale Computing - EPASA 2015
PublisherSpringer Verlag
Pages143-155
Number of pages13
ISBN (Print)9783319624242
DOIs
Publication statusPublished - 2017 Jan 1
Event1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015 - Tsukuba, Japan
Duration: 2015 Sep 142015 Sep 16

Publication series

NameLecture Notes in Computational Science and Engineering
Volume117
ISSN (Print)1439-7358

Other

Other1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015
CountryJapan
CityTsukuba
Period15/9/1415/9/16

Fingerprint

Eigenvalues and eigenfunctions

ASJC Scopus subject areas

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

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

Computation of eigenvectors for a specially structured banded matrix. / Takeuchi, Hiroshi; Aihara, Kensuke; Fukuda, Akiko; Ishiwata, Emiko.

Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. Springer Verlag, 2017. p. 143-155 (Lecture Notes in Computational Science and Engineering; Vol. 117).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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. 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 Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. Springer Verlag. 2017. p. 143-155. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-319-62426-6_10
Takeuchi, Hiroshi ; Aihara, Kensuke ; Fukuda, Akiko ; Ishiwata, Emiko. / Computation of eigenvectors for a specially structured banded matrix. Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. Springer Verlag, 2017. pp. 143-155 (Lecture Notes in Computational Science and Engineering).
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