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Extra Regularity of Hermite Subdivision Schemes

Abstract : Hermite subdivision schemes act on vector valued data that is not only considered as functions values of a vector valued function from R to R r , but as evaluations of a function and its consecutive derivatives. Starting with data on r (Z), r = d + 1, interpreted as function value and d = r − 1 consecutive derivatives, we compute successive iterations to define values on r (2 −n Z) and an r-vector valued limit function for whose first component C d-smoothness is generally expected. In this paper, we construct Hermite subdivision schemes such that, beginning with the same data, it is possible to reach a limit function with smoothness d +p for any p > 0. The result is obtained with a generalized Taylor factorization and a smoothness condition for vector subdivision schemes.
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https://hal.archives-ouvertes.fr/hal-03095865
Contributor : Jean-Louis Merrien <>
Submitted on : Monday, January 4, 2021 - 5:50:43 PM
Last modification on : Saturday, January 9, 2021 - 3:09:09 AM

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  • HAL Id : hal-03095865, version 1

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Jean-Louis Merrien, Tomas Sauer. Extra Regularity of Hermite Subdivision Schemes. 2021. ⟨hal-03095865⟩

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