153163 20251017144630.0 doi 10.3934/math.2025110 sideral 143619 ART-2025-143619 eng Díaz, Pablo Universidad de Zaragoza Total positivity, Gramian matrices, and Schur polynomials 2025 Access copy available to the general public Unrestricted This 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 info:eu-repo/grantAgreement/ES/DGA/E41-23R info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00 info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Mainar, Esmeralda Universidad de Zaragoza (orcid)0000-0002-1101-6230 Rubio, Beatriz Universidad de Zaragoza (orcid)0000-0001-9130-0794 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 10, 2 (2025), 2375-2391 AIMS Mathematics 2473-6988 301175 http://zaguan.unizar.es/record/153163/files/texto_completo.pdf Versión publicada 1882822 http://zaguan.unizar.es/record/153163/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:153163 articulos driver 2025-10-17-14:26:15 ARTICLE