A new equivalence notion between non-stationary subdivision schemes, termed asymptotic similarity, which is weaker than asymptotic equivalence, is introduced and studied. It is known that asymptotic 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 asymptotic equivalence can be relaxed to asymptotic similarity. This result applies to a wide class of non-stationary schemes.
Convergence of univariate non-stationary subdivision schemes via asymptotical similarity / Conti, Costanza; Dyn, Nira; Manni, Carla; Mazure, Marie-Laurence. - In: COMPUTER AIDED GEOMETRIC DESIGN. - ISSN 0167-8396. - STAMPA. - 37:(2015), pp. 1-8. [10.1016/j.cagd.2015.06.004]
Convergence of univariate non-stationary subdivision schemes via asymptotical similarity
CONTI, COSTANZA;
2015
Abstract
A new equivalence notion between non-stationary subdivision schemes, termed asymptotic similarity, which is weaker than asymptotic equivalence, is introduced and studied. It is known that asymptotic 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 asymptotic equivalence can be relaxed to asymptotic similarity. This result applies to a wide class of non-stationary schemes.File | Dimensione | Formato | |
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