@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 = "Universiteit Twente",

number = "1457",

}