An isospectral transformation between Hessenberg matrix and Hessenberg-bidiagonal matrix pencil without using subtraction
Numerical Analysis
2025-05-06 v2 Numerical Analysis
Spectral Theory
Exactly Solvable and Integrable Systems
Abstract
We introduce an eigenvalue-preserving transformation algorithm from the generalized eigenvalue problem by matrix pencil of the upper and the lower bidiagonal matrices into a standard eigenvalue problem while preserving sparsity, using the theory of orthogonal polynomials. The procedure is formulated without subtraction, which causes numerical instability. Furthermore, the algorithm is discussed for the extended case where the upper bidiagonal matrix is of Hessenberg type.
Cite
@article{arxiv.2212.11577,
title = {An isospectral transformation between Hessenberg matrix and Hessenberg-bidiagonal matrix pencil without using subtraction},
author = {Katsuki Kobayashi and Kazuki Maeda and Satoshi Tsujimoto},
journal= {arXiv preprint arXiv:2212.11577},
year = {2025}
}
Comments
21 pages