@article{ac1f31ddc4a2406c8c8de89110840d92,
title = "Convergence Acceleration of Shifted LR Transformations for Totally Nonnegative Hessenberg Matrices",
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.",
keywords = "34B16, 34C25, LR transformation, Newton shift, convergence rate, totally nonnegative matrix",
author = "Akiko Fukuda and Yusaku Yamamoto and Masashi Iwasaki and Emiko Ishiwata and Yoshimasa Nakamura",
note = "Funding Information: This research was partially supported by Grants-in-Aid for Scientific Research {\textcopyright} Number 19K03624 from the Japan Society for the Promotion of Science. Publisher Copyright: {\textcopyright} 2020, Mathematical Institute Academy of Sciences of Cz. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = oct,
day = "1",
doi = "10.21136/AM.2020.0378-19",
language = "English",
volume = "65",
pages = "677--702",
journal = "Applications of Mathematics",
issn = "0862-7940",
publisher = "Springer Netherlands",
number = "5",
}