%0 Journal Article
%A Branquinho, Amílcar
%A Foulquié Moreno, Ana
%A Mañas Baena, Manuel Enrique
%T Positive bidiagonal factorization of tetradiagonal Hessenberg matrices
%D 2023
%@ 0024-3795
%U https://hdl.handle.net/20.500.14352/102905
%X 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.
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