Accurate matrix conversion between Bernstein and ℎ-Bernstein bases

Khiar, Y. (Universidad de Zaragoza) ; Mainar, E. (Universidad de Zaragoza) ; Peña, J.M. (Universidad de Zaragoza) ; Royo-Amondarain, E. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.cagd.2026.102518

Año: 2026

Publicado en: Computer Aided Geometric Design 125 (2026), 102518 [7 pp.]
ISSN: 0167-8396

Financiación: info:eu-repo/grantAgreement/ES/DGA/E41-23R
Financiación: info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00
Financiación: info:eu-repo/grantAgreement/ES/MCIU/RED2022-134176-T

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)