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 ≥ dFile | Dimensione | Formato | |
---|---|---|---|
Conti_Merrien_Romani_REV_0603.pdf
Solo gestori archivio
Tipologia di allegato:
Author’s Accepted Manuscript, AAM (Post-print)
Dimensione
253.08 kB
Formato
Adobe PDF
|
253.08 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.