# Convergence Acceleration of Shifted LR Transformations for Totally Nonnegative Hessenberg Matrices

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

## 抄録

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.

本文言語 English 677-702 26 Applications of Mathematics 65 5 https://doi.org/10.21136/AM.2020.0378-19 Published - 2020 10月 1

• 応用数学

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