Convergence Acceleration of Shifted LR Transformations for Totally Nonnegative Hessenberg Matrices

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

Research output: Contribution to journalArticlepeer-review

Abstract

We design shifted LR transformations based on the integrable discrete hungry Toda equation to compute eigenvalues of totally nonnegative matrices of the banded Hessenberg form. The shifted LR transformation can be regarded as an extension of the extension employed in the well-known dqds algorithm for the symmetric tridiagonal eigenvalue problem. In this paper, we propose a new and effective shift strategy for the sequence of shifted LR transformations by considering the concept of the Newton shift. We show that the shifted LR transformations with the resulting shift strategy converge with order 2 − ε for arbitrary ε > 0.

Original languageEnglish
Pages (from-to)677-702
Number of pages26
JournalApplications of Mathematics
Volume65
Issue number5
DOIs
Publication statusPublished - 2020 Oct 1

Keywords

  • 34B16
  • 34C25
  • convergence rate
  • LR transformation
  • Newton shift
  • totally nonnegative matrix

ASJC Scopus subject areas

  • Applied Mathematics

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