Totally positive Wronskian matrices and symmetric functions

Díaz, Pablo (Universidad de Zaragoza) ; Mainar, Esmeralda (Universidad de Zaragoza) ; Rubio, Beatriz (Universidad de Zaragoza)

Resumen: The elements of the bidiagonal decomposition (BD) of a totally positive (TP) collocation matrix can be expressed in terms of symmetric functions of the nodes. Making use of this result, and studying the relation between Wronskian and collocation matrices of a given TP basis of functions, we can express the entries of the BD of Wronskian matrices as the values of certain symmetric functions evaluated at a single node. Moreover, in the case of polynomial bases, we obtain compact formulae for the entries of the BD of their Wronskian matrices. Interesting examples illustrate the applications of the obtained formulae.

Idioma: Inglés

DOI: 10.3390/axioms13090589

Año: 2024

Publicado en: Axioms 13, 9 (2024), 589 [14 pp.]
ISSN: 2075-1680

Financiación: info:eu-repo/grantAgreement/ES/DGA/E41-23R
Financiación: info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00
Financiación: info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)