Positive bidiagonal factorization of tetradiagonal Hessenberg matrices

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 pos...

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Bibliographic Details
Published in:Linear algebra and its applications 2023-11, Vol.677, p.132-160
Main Authors: Branquinho, Amílcar, Foulquié-Moreno, Ana, Mañas, Manuel
Format: Article
Language:English
Subjects:
Banded Hessenberg matrices
Bidiagonal factorization
Continued fractions
Gauss–Borel factorization
Oscillatory matrices
Oscillatory retracted matrices
Totally nonnegative matrices
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Summary: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2023.08.001