Though a Hermite subdivision scheme is non-stationary by nature, its non-stationarity can be of two types, making useful the distinction between Inherently Stationary and Inherently Non-Stationary Hermite subdivision schemes. This paper focuses on the class of inherently stationary, dual non-interpolatory Hermite subdivision schemes that can be obtained from known Hermite interpolatory ones, by applying a generalization of the de Rham corner cutting strategy. Exploiting specific tools for the analysis of inherently stationary Hermite subdivision schemes we show that, giving up the interpolation condition, the smoothness of the associated basic limit function can be increased by one, while its support width is only enlarged by one. To accomplish the analysis of de Rham-type Hermite subdivision schemes two new theoretical results are derived and the new notion of HCℓ-convergence is introduced. It allows the construction of Hermite-type subdivision schemes of order d+1 with the first element of the vector valued limit function having regularity ℓ ≥ d

Conti, C., Merrien, J., Romani, L. (2014). Dual Hermite Subdivision Schemes of de Rham-type. BIT, 54(4), 955-977 [10.1007/s10543-014-0495-z].

Dual Hermite Subdivision Schemes of de Rham-type

ROMANI, LUCIA
2014

Abstract

Though a Hermite subdivision scheme is non-stationary by nature, its non-stationarity can be of two types, making useful the distinction between Inherently Stationary and Inherently Non-Stationary Hermite subdivision schemes. This paper focuses on the class of inherently stationary, dual non-interpolatory Hermite subdivision schemes that can be obtained from known Hermite interpolatory ones, by applying a generalization of the de Rham corner cutting strategy. Exploiting specific tools for the analysis of inherently stationary Hermite subdivision schemes we show that, giving up the interpolation condition, the smoothness of the associated basic limit function can be increased by one, while its support width is only enlarged by one. To accomplish the analysis of de Rham-type Hermite subdivision schemes two new theoretical results are derived and the new notion of HCℓ-convergence is introduced. It allows the construction of Hermite-type subdivision schemes of order d+1 with the first element of the vector valued limit function having regularity ℓ ≥ d
Articolo in rivista - Articolo scientifico
Vector subdivision; Inherently stationary Hermite subdivision; de Rham strategy; Dual parametrization; Convergence and smoothness analysis.
English
2014
BIT
54
4
955
977
reserved
Conti, C., Merrien, J., Romani, L. (2014). Dual Hermite Subdivision Schemes of de Rham-type. BIT, 54(4), 955-977 [10.1007/s10543-014-0495-z].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/52911
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