Extra Regularity of Hermite Subdivision Schemes

Abstract

Hermite subdivision schemes act on vector valued sequences that are not only considered as functions values of a vector valued function from R to Rr , 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-nZ) and an r-vector valued limit function for whose first component Cd–smoothness is generally expected. In this paper, we construct univariate Hermite subdivision schemes such that, for any given initial 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.

Merrien J., Sauer T. (2021) "Extra Regularity of Hermite Subdivision Schemes " Dolomites Research Notes on Approximation, 14(2), 85-94. DOI: 10.14658/PUPJ-DRNA-2021-2-10  
Year of Publication
2021
Journal
Dolomites Research Notes on Approximation
Volume
14
Issue Number
2
Start Page
85
Last Page
94
Date Published
04/2021
ISSN Number
2035-6803
Serial Article Number
10
DOI
10.14658/PUPJ-DRNA-2021-2-10
Issue
Section
SpecialIssue