000169230 001__ 169230 000169230 005__ 20260223164759.0 000169230 0247_ $$2doi$$a10.1016/j.cagd.2026.102518 000169230 0248_ $$2sideral$$a148272 000169230 037__ $$aART-2026-148272 000169230 041__ $$aeng 000169230 100__ $$0(orcid)0000-0002-6497-7158$$aKhiar, Y.$$uUniversidad de Zaragoza 000169230 245__ $$aAccurate matrix conversion between Bernstein and ℎ-Bernstein bases 000169230 260__ $$c2026 000169230 5060_ $$aAccess copy available to the general public$$fUnrestricted 000169230 5203_ $$aThis 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. 000169230 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E41-23R$$9info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00$$9info:eu-repo/grantAgreement/ES/MCIU/RED2022-134176-T 000169230 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc$$uhttps://creativecommons.org/licenses/by-nc/4.0/deed.es 000169230 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000169230 700__ $$0(orcid)0000-0002-1101-6230$$aMainar, E.$$uUniversidad de Zaragoza 000169230 700__ $$0(orcid)0000-0002-1340-0666$$aPeña, J.M.$$uUniversidad de Zaragoza 000169230 700__ $$0(orcid)0000-0003-1550-8168$$aRoyo-Amondarain, E.$$uUniversidad de Zaragoza 000169230 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000169230 773__ $$g125 (2026), 102518 [7 pp.]$$pComput. aided geom. des.$$tComputer Aided Geometric Design$$x0167-8396 000169230 8564_ $$s1535106$$uhttps://zaguan.unizar.es/record/169230/files/texto_completo.pdf$$yVersión publicada 000169230 8564_ $$s1689886$$uhttps://zaguan.unizar.es/record/169230/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000169230 909CO $$ooai:zaguan.unizar.es:169230$$particulos$$pdriver 000169230 951__ $$a2026-02-23-14:54:58 000169230 980__ $$aARTICLE