Dimension elevation formula for Chebyshevian blossoms

Authors:
Marie-Laurence Mazure
Affiliations:
Laboratoire Jean Kuntzmann, Université Joseph Fourier, BP53, 38041 Grenoble Cedex 9, France
Venue:
Computer Aided Geometric Design
Year:
2009

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Abstract

A given polynomial of degree less than or equal to n naturally ''blossoms'' into a function of n variables called its blossom. Considered as a polynomial function of degree less than or equal to (n+1) it ''blossoms'' into a ''new'' blossom which is now a function of (n+1) variables. A classical formula expresses any value of this new blossom as a strictly convex combination of (n+1) values of the initial one. We establish a similar formula for Chebyshevian blossoms.