Bidiagonal Factorizations of Filbert and Lilbert Matrices

Khiar, Yasmina (Universidad de Zaragoza) ; Mainar, Esmeralda (Universidad de Zaragoza) ; Peña, Juan Manuel (Universidad de Zaragoza) ; Royo-Amondarain, Eduardo (Universidad de Zaragoza) ; Rubio, Beatriz (Universidad de Zaragoza)

Resumen: Extensions of Filbert and Lilbert matrices are addressed in this work. They are reciprocal Hankel matrices based on Fibonacci and Lucas numbers, respectively, and both are related to Hilbert matrices. The Neville elimination is applied to provide explicit expressions for their bidiagonal factorization. As a byproduct, formulae for the determinants of these matrices are obtained. Finally, numerical experiments show that several algebraic problems involving these matrices can be solved with outstanding accuracy, in contrast with traditional approaches.

Idioma: Inglés

DOI: 10.3390/axioms13040219

Año: 2024

Publicado en: Axioms 13, 4 (2024), 219 [14 pp.]
ISSN: 2075-1680

Financiación: info:eu-repo/grantAgreement/ES/DGA/E41-23R
Financiación: info:eu-repo/grantAgreement/ES/DGA/S60-23R
Financiación: info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00
Financiación: info:eu-repo/grantAgreement/ES/MCIU/RED2022-134176-T

Tipo y forma: Article (Published version)

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