Bidiagonal factorization of tetradiagonal matrices and Darboux transformations

Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory. In this paper the Lima-Loureiro hypergeometric multiple orthogonal polynomials and the Jacobi-Pineiro multiple orthogo...

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Detalles Bibliográficos
Autores: Branquinho, Amilcar, Foulquié Moreno, Ana, Mañas Baena, Manuel Enrique
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/72313
Acceso en línea:https://hdl.handle.net/20.500.14352/72313
Access Level:acceso abierto
Palabra clave:51-73
Tetradiagonal Hessenberg matrices
Oscillatory matrices
Totally nonnegative matrices
Multiple orthogonal polynomials
Favard spectral representation
Darboux transformations
Christoffel formulas
Física-Modelos matemáticos
Física matemática
Descripción
Sumario:Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory. In this paper the Lima-Loureiro hypergeometric multiple orthogonal polynomials and the Jacobi-Pineiro multiple orthogonal polynomials are discussed at the light of this bidiagonal factorization for tetradiagonal matrices. The Darboux transformations of tetradiagonal Hessenberg matrices is studied and Christoffel formulas for the elements of the bidiagonal factorization are given, i.e., the bidiagonal factorization is given in terms of the recursion polynomials evaluated at the origin.