161919 20251017144652.0 doi 10.1007/s40324-025-00392-w sideral 144583 ART-2025-144583 eng Khiar, Y. Universidad de Zaragoza (orcid)0000-0002-6497-7158 On the accurate basis conversion of univariate polynomials 2025 Access copy available to the general public Unrestricted This paper summarizes the bidiagonal factorizations of change of basis matrices between polynomial bases commonly used in interpolation and computer-aided geometric design. These factorizations enable the efficient and highly accurate resolution of linear algebra problems, offering significant advantages in terms of precision. The article also highlights a variety of applications, including the accurate computation of divided differences and the efficient solution of algebraic problems involving collocation matrices or Gram matrices, underscoring the practical relevance of these factorizations in mathematical and computational contexts. info:eu-repo/grantAgreement/ES/DGA/E41-23R info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00 info:eu-repo/grantAgreement/ES/MCIU/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, E. Universidad de Zaragoza (orcid)0000-0002-1101-6230 Peña, J. M. Universidad de Zaragoza (orcid)0000-0002-1340-0666 Royo-Amondarain, E. Universidad de Zaragoza (orcid)0000-0003-1550-8168 Rubio, B. Universidad de Zaragoza (orcid)0000-0001-9130-0794 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada (2025), 23 pp. SEMA j. SEMA Journal 2254-3902 616631 http://zaguan.unizar.es/record/161919/files/texto_completo.pdf Versión publicada 1239864 http://zaguan.unizar.es/record/161919/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:161919 articulos driver 2025-10-17-14:36:41 ARTICLE