RT Journal Article
T1 Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
A1 Branquinho, Amilcar
A1 Foulquié Moreno, Ana
A1 Mañas Baena, Manuel Enrique
AB 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.
PB Springer Basel AG
SN 1664-2368
YR 2023
FD 2023-06
LK https://hdl.handle.net/20.500.14352/72313
UL https://hdl.handle.net/20.500.14352/72313
LA eng
NO CRUE-CSIC (Acuerdos Transformativos 2023)© The Author(s) 2023Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Amilcar Branquinho thanks Centre for Mathematics of the University of Coimbra-UIDB/00324/2020 (funded by the Portuguese Government through FCT/MCTES) and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020Ana Foulquie acknowledges Center for Research & Development in Mathematics and Applications, supported through the Portuguese Foundation for Science and Technology (FCT- Fundacao para a Ciencia e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020. Manuel Manas: Thanks financial support from the Spanish "Agencia Estatal de Investigacion" research project [PGC2018-096504-B-C33], Ortogonalidad y Aproximacion: Teoria y Aplicaciones en Fisica Matematica and [PID2021- 122154NB-I00], Ortogonalidad y Aproximacion con Aplicaciones en Machine Learning y Teoria de la Probabilidad.
NO Ministerio de Ciencia e Innovación (MICINN)/AEI
NO Ministerio de Cienncia e Innovación (MICINN)
NO Fundação para a Ciência e a Tecnologia (FCT)
NO Center for Mathematics of the University of Coimbra
NO Portuguese Government through FCT/MCTES
DS Docta Complutense
RD 10 abr 2025