000127992 001__ 127992
000127992 005__ 20240122154817.0
000127992 0247_ $$2doi$$a10.1002/nla.2521
000127992 0248_ $$2sideral$$a135102
000127992 037__ $$aART-2023-135102
000127992 041__ $$aeng
000127992 100__ $$0(orcid)0000-0002-1101-6230$$aMainar, E.$$uUniversidad de Zaragoza
000127992 245__ $$aTotal positivity and accurate computations with Gram matrices of Said-Ball bases
000127992 260__ $$c2023
000127992 5060_ $$aAccess copy available to the general public$$fUnrestricted
000127992 5203_ $$aIn 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.
000127992 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E41-23R$$9info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00$$9info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T
000127992 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000127992 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000127992 700__ $$0(orcid)0000-0002-1340-0666$$aPeña, J.M.$$uUniversidad de Zaragoza
000127992 700__ $$0(orcid)0000-0001-9130-0794$$aRubio, B.$$uUniversidad de Zaragoza
000127992 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000127992 773__ $$g30, 6 (2023), e2521 [17 pp.]$$pNumer. linear algebra appl.$$tNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS$$x1070-5325
000127992 8564_ $$s1960184$$uhttps://zaguan.unizar.es/record/127992/files/texto_completo.pdf$$yVersión publicada
000127992 8564_ $$s2538908$$uhttps://zaguan.unizar.es/record/127992/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000127992 909CO $$ooai:zaguan.unizar.es:127992$$particulos$$pdriver
000127992 951__ $$a2024-01-22-15:43:57
000127992 980__ $$aARTICLE