000153163 001__ 153163 000153163 005__ 20251017144630.0 000153163 0247_ $$2doi$$a10.3934/math.2025110 000153163 0248_ $$2sideral$$a143619 000153163 037__ $$aART-2025-143619 000153163 041__ $$aeng 000153163 100__ $$aDíaz, Pablo$$uUniversidad de Zaragoza 000153163 245__ $$aTotal positivity, Gramian matrices, and Schur polynomials 000153163 260__ $$c2025 000153163 5060_ $$aAccess copy available to the general public$$fUnrestricted 000153163 5203_ $$aThis paper investigated the total positivity of Gramian matrices associated with general bases of functions. It demonstrated that the total positivity of collocation matrices for totally positive bases extends to their Gramian matrices. Additionally, a bidiagonal decomposition of these Gramian matrices, derived from integrals of symmetric functions, was presented. This decomposition enables the design of algorithms with high relative accuracy for solving linear algebra problems involving totally positive Gramian matrices. For polynomial bases, compact and explicit formulas for the bidiagonal decomposition were provided, involving integrals of Schur polynomials. These integrals, known as Selberg-like integrals, arise naturally in various contexts within Physics and Mathematics 000153163 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E41-23R$$9info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00$$9info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T 000153163 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es 000153163 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000153163 700__ $$0(orcid)0000-0002-1101-6230$$aMainar, Esmeralda$$uUniversidad de Zaragoza 000153163 700__ $$0(orcid)0000-0001-9130-0794$$aRubio, Beatriz$$uUniversidad de Zaragoza 000153163 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000153163 773__ $$g10, 2 (2025), 2375-2391$$tAIMS Mathematics$$x2473-6988 000153163 8564_ $$s301175$$uhttps://zaguan.unizar.es/record/153163/files/texto_completo.pdf$$yVersión publicada 000153163 8564_ $$s1882822$$uhttps://zaguan.unizar.es/record/153163/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000153163 909CO $$ooai:zaguan.unizar.es:153163$$particulos$$pdriver 000153163 951__ $$a2025-10-17-14:26:15 000153163 980__ $$aARTICLE