169230 20260223164759.0 doi 10.1016/j.cagd.2026.102518 sideral 148272 ART-2026-148272 eng Khiar, Y. Universidad de Zaragoza (orcid)0000-0002-6497-7158 Accurate matrix conversion between Bernstein and ℎ-Bernstein bases 2026 This paper investigates the matrix conversion between the classical Bernstein basis and its oneparameter generalization, the ℎ-Bernstein basis. New ℎ-analogues of the binomial coefficients are introduced, providing explicit and compact expressions for the entries of the corresponding change-of-basis matrices. Structural properties such as symmetry and recurrence relations are derived, offering both theoretical insight and practical computational advantages. The proposed recurrence formulations enable the generation of the conversion matrices with high relative accuracy, avoiding subtractive cancellations and the numerical instabilities associated with direct collocation-based approaches. These results ensure reliable computations even for very large degrees and establish a foundation for the development of accurate and efficient algorithms in geometric modeling and related numerical applications involving ℎ-Bernstein polynomials. Numerical experiments confirm the theoretical findings and highlight the advantages of the proposed approach. Access copy available to the general public Unrestricted 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-nc https://creativecommons.org/licenses/by-nc/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 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 125 (2026), 102518 [7 pp.] Comput. aided geom. des. Computer Aided Geometric Design 0167-8396 1535106 http://zaguan.unizar.es/record/169230/files/texto_completo.pdf Versión publicada 1689886 http://zaguan.unizar.es/record/169230/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:169230 articulos driver 2026-02-23-14:54:58 ARTICLE