Total Positivity and Accurate Computations Related to q-Abel Polynomials

Khiar, Y. (Universidad de Zaragoza) ; Mainar, E. (Universidad de Zaragoza) ; Royo-Amondarain, E. (Universidad de Zaragoza) ; Rubio, B. (Universidad de Zaragoza)

Resumen: The attainment of accurate numerical solutions of ill-conditioned linear algebraic problems involving totally positive matrices has been gathering considerable attention among researchers over the last years. In parallel, the interest of q-calculus has been steadily growing in the literature. In this work the q-analogue of the Abel polynomial basis is studied. The total positivity of the matrix of change of basis between monomial and q-Abel bases is characterized, providing its bidiagonal factorization. Moreover, well-known high relative accuracy results of Vandermonde matrices corresponding to increasing positive nodes are extended to the decreasing negative case. This further allows to solve with high relative accuracy several algebraic problems concerning collocation, Wronskian and Gramian matrices of q-Abel polynomials. Finally, a series of numerical tests support the presented theoretical results and illustrate the goodness of the method where standard approaches fail to deliver accurate solutions.

Idioma: Inglés

DOI: 10.1007/s10915-024-02699-8

Año: 2024

Publicado en: Journal of Scientific Computing 101 (2024), 1-22
ISSN: 0885-7474

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: Artículo (Versión definitiva)

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