000161919 001__ 161919 000161919 005__ 20251017144652.0 000161919 0247_ $$2doi$$a10.1007/s40324-025-00392-w 000161919 0248_ $$2sideral$$a144583 000161919 037__ $$aART-2025-144583 000161919 041__ $$aeng 000161919 100__ $$0(orcid)0000-0002-6497-7158$$aKhiar, Y.$$uUniversidad de Zaragoza 000161919 245__ $$aOn the accurate basis conversion of univariate polynomials 000161919 260__ $$c2025 000161919 5060_ $$aAccess copy available to the general public$$fUnrestricted 000161919 5203_ $$aThis 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. 000161919 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E41-23R$$9info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00$$9info:eu-repo/grantAgreement/ES/MCIU/RED2022-134176-T 000161919 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es 000161919 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000161919 700__ $$0(orcid)0000-0002-1101-6230$$aMainar, E.$$uUniversidad de Zaragoza 000161919 700__ $$0(orcid)0000-0002-1340-0666$$aPeña, J. M.$$uUniversidad de Zaragoza 000161919 700__ $$0(orcid)0000-0003-1550-8168$$aRoyo-Amondarain, E.$$uUniversidad de Zaragoza 000161919 700__ $$0(orcid)0000-0001-9130-0794$$aRubio, B.$$uUniversidad de Zaragoza 000161919 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000161919 773__ $$g(2025), 23 pp.$$pSEMA j.$$tSEMA Journal$$x2254-3902 000161919 8564_ $$s616631$$uhttps://zaguan.unizar.es/record/161919/files/texto_completo.pdf$$yVersión publicada 000161919 8564_ $$s1239864$$uhttps://zaguan.unizar.es/record/161919/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000161919 909CO $$ooai:zaguan.unizar.es:161919$$particulos$$pdriver 000161919 951__ $$a2025-10-17-14:36:41 000161919 980__ $$aARTICLE