127992 20241125101201.0 doi 10.1002/nla.2521 sideral 135102 ART-2023-135102 eng Mainar, E. Universidad de Zaragoza (orcid)0000-0002-1101-6230 Total positivity and accurate computations with Gram matrices of Said-Ball bases 2023 Access copy available to the general public Unrestricted 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. info:eu-repo/grantAgreement/ES/DGA/E41-23R info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00 info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 1.8 2023 MATHEMATICS, APPLIED 75 / 332 = 0.226 2023 Q1 T1 MATHEMATICS 39 / 490 = 0.08 2023 Q1 T1 0.932 2023 Applied Mathematics 2023 Q1 Algebra and Number Theory 2023 Q1 3.4 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Peña, J.M. Universidad de Zaragoza (orcid)0000-0002-1340-0666 Rubio, B. Universidad de Zaragoza (orcid)0000-0001-9130-0794 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 30, 6 (2023), e2521 [17 pp.] Numer. linear algebra appl. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 1070-5325 1960184 http://zaguan.unizar.es/record/127992/files/texto_completo.pdf Versión publicada 2538908 http://zaguan.unizar.es/record/127992/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:127992 articulos driver 2024-11-22-12:11:33 ARTICLE