Polynomial Total Positivity and High Relative Accuracy Through Schur Polynomials

Díaz, P. (Universidad de Zaragoza) ; Mainar, E. (Universidad de Zaragoza) ; Rubio, B. (Universidad de Zaragoza)

Resumen: In this paper, Schur polynomials are used to provide a bidiagonal decomposition of polynomial collocation matrices. The symmetry of Schur polynomials is exploited to analyze the total positivity on some unbounded intervals of a relevant class of polynomial bases. The proposed factorization is used to achieve relative errors of the order of the unit round-off when solving algebraic problems involving the collocation matrix of relevant polynomial bases, such as the Hermite basis. The numerical experimentation illustrates the accurate results obtained when using the findings of the paper.

Idioma: Inglés

DOI: 10.1007/s10915-023-02323-1

Año: 2023

Publicado en: Journal of Scientific Computing 97, 10 (2023), [27 pp.]
ISSN: 0885-7474

Financiación: info:eu-repo/grantAgreement/ES/DGA/E41-23R
Financiación: info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-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)