Eigenvalue computation of totally nonnegative upper Hessenberg matrices based on a variant of the discrete hungry Toda equation

Ryo Sumikura, Akiko Fukuda, Emiko Ishiwata, Yusaku Yamamoto, Masashi Iwasaki, Yoshimasa Nakamura

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

2 Citations (Scopus)

Abstract

The integrable discrete hungry Toda (dhToda) equation has already been applied to design an eigenvalue algorithm which computes eigenvalues of totally nonnegative (TN) matrices with lower Hessenberg form. In this paper, an eigenvalue algorithm for computing eigenvalues of TN matrices with upper Hessenberg form is derived based on a variant of the dhToda equation.

Original languageEnglish
Title of host publicationAIP Conference Proceedings
PublisherAmerican Institute of Physics Inc.
Volume1648
ISBN (Print)9780735412873
DOIs
Publication statusPublished - 2015 Mar 10
EventInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 - Rhodes, Greece
Duration: 2014 Sep 222014 Sep 28

Other

OtherInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
CountryGreece
CityRhodes
Period14/9/2214/9/28

Fingerprint

eigenvalues
matrices

Keywords

  • discrete hungry Toda equation
  • eigenvalue
  • totally nonnegative matrix

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Sumikura, R., Fukuda, A., Ishiwata, E., Yamamoto, Y., Iwasaki, M., & Nakamura, Y. (2015). Eigenvalue computation of totally nonnegative upper Hessenberg matrices based on a variant of the discrete hungry Toda equation. In AIP Conference Proceedings (Vol. 1648). [690006] American Institute of Physics Inc.. https://doi.org/10.1063/1.4912921

Eigenvalue computation of totally nonnegative upper Hessenberg matrices based on a variant of the discrete hungry Toda equation. / Sumikura, Ryo; Fukuda, Akiko; Ishiwata, Emiko; Yamamoto, Yusaku; Iwasaki, Masashi; Nakamura, Yoshimasa.

AIP Conference Proceedings. Vol. 1648 American Institute of Physics Inc., 2015. 690006.

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

Sumikura, R, Fukuda, A, Ishiwata, E, Yamamoto, Y, Iwasaki, M & Nakamura, Y 2015, Eigenvalue computation of totally nonnegative upper Hessenberg matrices based on a variant of the discrete hungry Toda equation. in AIP Conference Proceedings. vol. 1648, 690006, American Institute of Physics Inc., International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014, Rhodes, Greece, 14/9/22. https://doi.org/10.1063/1.4912921
Sumikura R, Fukuda A, Ishiwata E, Yamamoto Y, Iwasaki M, Nakamura Y. Eigenvalue computation of totally nonnegative upper Hessenberg matrices based on a variant of the discrete hungry Toda equation. In AIP Conference Proceedings. Vol. 1648. American Institute of Physics Inc. 2015. 690006 https://doi.org/10.1063/1.4912921
Sumikura, Ryo ; Fukuda, Akiko ; Ishiwata, Emiko ; Yamamoto, Yusaku ; Iwasaki, Masashi ; Nakamura, Yoshimasa. / Eigenvalue computation of totally nonnegative upper Hessenberg matrices based on a variant of the discrete hungry Toda equation. AIP Conference Proceedings. Vol. 1648 American Institute of Physics Inc., 2015.
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