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: Article (Published version)
Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes.
Exportado de SIDERAL (2026-02-23-14:54:58)
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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: Article (Published version)
Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. Exportado de SIDERAL (2026-02-23-14:54:58)
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Record created 2026-02-23, last modified 2026-02-23