On the accuracy of de Casteljau-type algorithms and Bernstein representations

Delgado, J. (Universidad de Zaragoza) ; Mainar, E. (Universidad de Zaragoza) ; Peña, J.M. (Universidad de Zaragoza)

Resumen: This paper summarizes interesting results on systematic backward and forward error analyses performed for corner cutting algorithms providing evaluation of univariate and multivariate functions defined in terms of Bernstein and Bernstein related bases. Relevant results on the conditioning of the bases are also recalled. Finally, the paper surveys important advances, lately obtained, for the design of algorithms adapted to the structure of totally positive matrices, allowing the resolution of interpolation and approximation problems with Bernstein-type bases achieving computations to high relative accuracy.

Idioma: Inglés

DOI: 10.1016/j.cagd.2023.102243

Año: 2023

Publicado en: Computer Aided Geometric Design 106 (2023), 102243 [14 pp.]
ISSN: 0167-8396

Tipo y forma: Article (Published version)

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