Positive bidiagonal factorization of tetradiagonal Hessenberg matrices

2022/10/13 by Branquinho, Amílcar, Foulquié-Moreno, Ana, Mañas, Manuel · 2 citations
#15B48 #33C45 #33C47 #42C05 #47B28 #47B36 #47B39 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2210.10728

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.

Cited by

• Uvarov Perturbations for Multiple Orthogonal Polynomials of the Mixed Type on the Step-Line
• Bivariate multiple orthogonal polynomials of mixed type on the step-line

Related

• Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
• Banded matrices and their orthogonality
• Spectral theory for bounded banded matrices with positive bidiagonal factorization and mixed multiple orthogonal polynomials
• Oscillatory banded Hessenberg matrices, multiple orthogonal polynomials and random walks
• A note on banded linear systems