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. (C) 2015 Elsevier B.V. All rights reserved.
Conti, C., Dyn, N., Manni, C., Mazure, M.-. (2015). Convergence of univariate non-stationary subdivision schemes via asymptotic similarity. COMPUTER AIDED GEOMETRIC DESIGN, 37, 1-8 [10.1016/j.cagd.2015.06.004].
Convergence of univariate non-stationary subdivision schemes via asymptotic similarity
Manni C.Membro del Collaboration Group
;
2015-01-01
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. (C) 2015 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
