Increasing the smoothness of vector and Hermite subdivision schemes. (29th March 2018)

• Record Type: Journal Article
• Authors: Moosmüller, Caroline; Dyn, Nira
• Is Part Of: IMA journal of numerical analysis. Volume 39:Number 2(2019)
• Page Start: 579
• Page End: 606
• Publication Date: 2018-03-29
• Subjects: vector subdivision schemes -- Hermite subdivision schemes -- symbol of a subdivision scheme -- smoothness -- analysis of limit functions; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/dry010
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: In this paper we suggest a method for transforming a vector subdivision scheme (VSS) generating C ℓ limits to another such scheme of the same dimension, generating C ℓ +1 limits. In scalar subdivision, it is well known that a scheme generating C ℓ limit curves can be transformed to a new scheme producing C ℓ +1 limit curves by multiplying the scheme's symbol with the smoothing factor $\tfrac{z+1}{2}$ . First we extend this approach to VSSs, by manipulating symbols. The algorithms presented in this paper allow us to construct VSSs of arbitrarily high regularity from a convergent vector scheme. Furthermore, from a certain class of converging Hermite schemes of dimension 2, we are able to obtain new Hermite schemes of dimension 2 with regularity of any order.