119832 20240319081006.0 doi 10.1007/s13398-022-01253-1 sideral 130706 ART-2022-130706 eng Mainar, E. Universidad de Zaragoza (orcid)0000-0002-1101-6230 Accurate computations with Gram and Wronskian matrices of geometric and Poisson bases 2022 Access copy available to the general public Unrestricted In this paper we deduce a bidiagonal decomposition of Gram and Wronskian matrices of geometric and Poisson bases. It is also proved that the Gram matrices of both bases are strictly totally positive, that is, all their minors are positive. The mentioned bidiagonal decompositions are used to achieve algebraic computations with high relative accuracy for Gram and Wronskian matrices of these bases. The provided numerical experiments illustrate the accuracy when computing the inverse matrix, the eigenvalues or singular values or the solutions of some linear systems, using the theoretical results. info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 2.9 2022 MATHEMATICS 15 / 329 = 0.046 2022 Q1 T1 0.933 2022 Algebra and Number Theory 2022 Q1 Analysis 2022 Q1 Geometry and Topology 2022 Q1 Computational Mathematics 2022 Q1 Applied Mathematics 2022 Q1 4.9 2022 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 116 (2022), 126 [22 pp.] Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 1578-7303 411977 http://zaguan.unizar.es/record/119832/files/texto_completo.pdf Versión publicada 1224263 http://zaguan.unizar.es/record/119832/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:119832 articulos driver 2024-03-18-14:37:35 ARTICLE