Treffer: Blossoms and Optimal Bases: Blossoms and optimal bases

Title:
Blossoms and Optimal Bases: Blossoms and optimal bases
Authors:
Marie-Laurence Mazure
Source:
Advances in Computational Mathematics. 20:177-203
Publisher Information:
Springer Science and Business Media LLC, 2004.
Publication Year:
2004
Subject Terms:
optimal bases, Spline approximation, total positivity, B-spline basis, blossoming, 0101 mathematics, extended Chebyshev spaces, corner cutting algorithms, 01 natural sciences, Numerical computation using splines
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
1572-9044
1019-7168
DOI:
10.1023/a:1025855123163
Access URL:
https://link.springer.com/article/10.1023/A:1025855123163
https://dblp.uni-trier.de/db/journals/adcm/adcm20.html#Mazure04
Rights:
Springer Nature TDM
Accession Number:
edsair.doi.dedup.....dbadc8c381bc24c8c328b7d9af694bdd
Database:
OpenAIRE

Weitere Informationen

Links between blossoms and optimal bases are studied, in a general context [cf. \textit{M.-L. Mazure}, Comput. Aided Geom. Design 16, 649--669 (1999; Zbl 0997.65022)]. The total positivity of the Bernstein basis follows from the properties of the polynomial blossoms, and its optimality from their geometrical meaning is shown. An extension to the Chebyshev and quasi-Chebyshev framework is given with examples of optimal normalized totally positive bases in this context. In the framework of Chebyshev or quasi-Chebyshev splines with connection matrices, it is shown that the existence of blossoms automatically leads to B-spline bases, which are the corresponding optimal normalized totally positive bases.