In this paper, we present an algebraic perspective of the de Rham transform of a binary subdivision scheme and propose an elegant strategy for constructing dual mm-ary approximating subdivision schemes of de Rham-type, starting from two primal schemes of arity mm and 2, respectively. On the one hand, this new strategy allows us to show that several existing dual corner-cutting subdivision schemes fit into a unified framework. On the other hand, the proposed strategy provides a straightforward algorithm for constructing new dual subdivision schemes having higher smoothness and higher polynomial reproduction capabilities with respect to the two given primal schemes.

Conti, C., Romani, L. (2013). Dual univariate m-ary subdivision schemes of de Rham-type. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 407(2), 443-456 [10.1016/j.jmaa.2013.05.009].

Dual univariate m-ary subdivision schemes of de Rham-type

ROMANI, LUCIA
2013

Abstract

In this paper, we present an algebraic perspective of the de Rham transform of a binary subdivision scheme and propose an elegant strategy for constructing dual mm-ary approximating subdivision schemes of de Rham-type, starting from two primal schemes of arity mm and 2, respectively. On the one hand, this new strategy allows us to show that several existing dual corner-cutting subdivision schemes fit into a unified framework. On the other hand, the proposed strategy provides a straightforward algorithm for constructing new dual subdivision schemes having higher smoothness and higher polynomial reproduction capabilities with respect to the two given primal schemes.
Articolo in rivista - Articolo scientifico
Linear subdivision; Arity m; Primal and dual parametrization; Smoothness; Polynomial reproduction
English
2013
407
2
443
456
open
Conti, C., Romani, L. (2013). Dual univariate m-ary subdivision schemes of de Rham-type. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 407(2), 443-456 [10.1016/j.jmaa.2013.05.009].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/44294
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