Positive bidiagonal factorization of tetradiagonal Hessenberg matrices
Abstract
Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. In this paper conditions, in terms of continued fractions, for an oscillatory tetradiagonal Hessenberg matrix to have such positive bidiagonal factorization are found. Oscillatory tetradiagonal Toeplitz matrices are taken as a case study of matrix that admits a positive bidiagonal factorization. Moreover, it is proved that oscillatory banded Hessenberg matrices are organized in rays, with the origin of the ray not having the positive bidiagonal factorization and all the interior points of the ray having such positive bidiagonal factorization.
Cite
@article{arxiv.2210.10728,
title = {Positive bidiagonal factorization of tetradiagonal Hessenberg matrices},
author = {Amílcar Branquinho and Ana Foulquié-Moreno and Manuel Mañas},
journal= {arXiv preprint arXiv:2210.10728},
year = {2022}
}
Comments
20 pages This is the second part of the splitting of the paper arXiv:2203.13578 into three