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Communication Dans Un Congrès Année : 2016

Convergence of dimension elevation algorithms : only a typical CAGD issue?

Résumé

A given nested sequence of Extended Chebyshev spaces possessing Bernstein bases generates an in nite dimension elevation algorithm transforming control polygons of any given level into control polygons of the next level. This situation is the natural generalisation of the so-called degree elevation for parametric polynomial curves. Proving the possible convergence of such algorithms (in the rough sense of uniform convergence to the underlying curves) is a typical CAGD issue. In this talk, we review our recent results on this difficult question, with special focus on Müntz spaces and rational spaces. In particular we present our finndings on the equivalence between convergence of a given dimension elevation algorithm and the uniform approximation of continuous functions by positive operators of the Bernstein-type naturally associated with the nested sequence. Surprisingly enough, in the case of rational spaces, we show that convergence is also connected with Polya-type theorems on positive polynomials.
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Dates et versions

hal-01408144 , version 1 (03-12-2016)

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  • HAL Id : hal-01408144 , version 1

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Marie-Laurence Mazure, Rachid Ait Haddou. Convergence of dimension elevation algorithms : only a typical CAGD issue?. SIGMA'2016, SMAI-SIGMA, Oct 2016, Marseille-Luminy, France. ⟨hal-01408144⟩
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