Total positivity and accurate computations with Gram matrices of Said-Ball bases

Mainar, E. (Universidad de Zaragoza) ; Peña, J.M. (Universidad de Zaragoza) ; Rubio, B. (Universidad de Zaragoza)

Resumen: In this article, it is proved that Gram matrices of totally positive bases of the space of polynomials of a given degree on a compact interval are totally positive. Conditions to guarantee computations to high relative accuracy with those matrices are also obtained. Furthermore, a fast and accurate algorithm to compute the bidiagonal factorization of Gram matrices of the Said-Ball bases is obtained and used to compute to high relative accuracy their singular values and inverses, as well as the solution of some linear systems associated with these matrices. Numerical examples are included.

Idioma: Inglés

DOI: 10.1002/nla.2521

Año: 2023

Publicado en: NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 30, 6 (2023), e2521 [17 pp.]
ISSN: 1070-5325

Factor impacto JCR: 1.8 (2023)

Categ. JCR: MATHEMATICS, APPLIED rank: 75 / 332 = 0.226 (2023) - Q1 - T1
Categ. JCR: MATHEMATICS rank: 39 / 490 = 0.08 (2023) - Q1 - T1

Factor impacto CITESCORE: 3.4 - Algebra and Number Theory (Q1) - Applied Mathematics (Q2)

Factor impacto SCIMAGO: 0.932 - Applied Mathematics (Q1) - Algebra and Number Theory (Q1)

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)