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Article Dans Une Revue Computer Aided Geometric Design Année : 2015

Convergence of univariate non-stationary subdivision schemes via asymptotical similarity

Résumé

A new equivalence notion between non-stationary subdivision schemes, termed "asymptotical similarity", which is weaker than asymptotical equivalence, is introduced and studied. It is known that asymptotical equivalence between a non-stationary subdivision scheme and a convergent stationary scheme guarantees the convergence of the non-stationary scheme. We show that for non-stationary schemes reproducing constants, the condition of asymptotical equivalence can be relaxed to asymptotical similarity. This result applies to a wide class of non-stationary schemes.
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Dates et versions

hal-00985115 , version 1 (29-04-2014)

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Costanza Conti, Nira Dyn, Carla Manni, Marie-Laurence Mazure. Convergence of univariate non-stationary subdivision schemes via asymptotical similarity. Computer Aided Geometric Design, 2015, 37, pp.1-8. ⟨10.1016/j.cagd.2015.06.004⟩. ⟨hal-00985115⟩
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