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Title: Positive bidiagonal factorization of tetradiagonal Hessenberg matrices
Author: Branquinho, Amílcar
Foulquié-Moreno, Ana
Mañas, Manuel
Keywords: Banded Hessenberg matrices
Oscillatory matrices
Totally nonnegative matrices
Continued fractions
Gauss–Borel factorization
Bidiagonal factorization
Oscillatory retracted matrices
Issue Date: 15-Nov-2023
Publisher: Elsevier
Abstract: Recently, a spectral Favard theorem was presented for bounded banded lower Hessenberg matrices that possess a positive bidiagonal factorization. The paper establishes conditions, expressed in terms of continued fractions, under which an oscillatory tetradiagonal Hessenberg matrix can have such a positive bidiagonal factorization. Oscillatory tetradiagonal Toeplitz matrices are examined as a case study of matrices that admit a positive bidiagonal factorization. Furthermore, the paper proves that oscillatory banded Hessenberg matrices are organized in rays, where the origin of the ray does not have a positive bidiagonal factorization, but all the interior points of the ray do have such a positive bidiagonal factorization.
Peer review: yes
DOI: 10.1016/j.laa.2023.08.001
ISSN: 0024-3795
Publisher Version:
Appears in Collections:CIDMA - Artigos
DMat - Artigos
CHAG - Artigos

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