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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Veröffentlicht in:Linear algebra and its applications Jg. 677; S. 132 - 160
Hauptverfasser: Branquinho, Amílcar, Foulquié-Moreno, Ana, Mañas, Manuel
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 15.11.2023
Schlagworte:
Banded Hessenberg matrices
Bidiagonal factorization
Continued fractions
Gauss–Borel factorization
Oscillatory matrices
Oscillatory retracted matrices
Totally nonnegative matrices
33C47
33C45
Oscillatory retracted matrices
15B48
Gauss–Borel factorization
Continued fractions
Bidiagonal factorization
Banded Hessenberg matrices
Totally nonnegative matrices
47B39
47B28
47B36
Oscillatory matrices
42C05
ISSN:0024-3795, 1873-1856
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Zusammenfassung: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