@book{c09a3be6064c4c3bb5cf3573a13b610a,
title = "Convexity preservation of the four-point interpolatory subdivision scheme",
abstract = "In this note we examine the convexity preserving properties of the (linear) four-point interpolatory subdivision scheme of Dyn, Gregory and Levin when applied to functional univariate strictly-convex data. Conditions on the tension parameter guaranteeing preservation of convexity are derived. These conditions depend on the initial data. The resulting scheme is the four-point scheme with tension parameter bounded from above by a bound smaller than $1/16$. Thus the scheme generates $C^1$ limit functions and has approximation order two.",
keywords = "MSC-41A29, METIS-141108, IR-30468, Convexity preservation, MSC-65D17, EWI-3277, Stationary subdivision scheme, MSC-65D05, MSC-41A05",
author = "Nira Dyn and F. Kuijt and David Levin and {van Damme}, {Rudolf M.J.}",
note = "Imported from MEMORANDA",
year = "1998",
language = "Undefined",
series = "Memorandum Faculteit TW",
publisher = "University of Twente",
number = "1457",
address = "Netherlands",
}