Smoothness of non-linear and non-separable subdivision schemes

Article type: Research Article

Authors: Matei, Basarab^; | Meignen, Sylvain | Zakharova, Anastasia

Affiliations: LAGA Laboratory, Paris XIII University, Paris, France | LJK Laboratory, University of Grenoble, Grenoble, France

Note: [] Corresponding author: Basarab Matei, LAGA Laboratory, Paris XIII University, Paris, France. Tel.: +33 1 49 40 35 71; Fax: +33 4 48 26 35 68; E-mail: [email protected].

Abstract: We study in this paper non-linear subdivision schemes in a multivariate setting allowing arbitrary dilation matrix. We investigate the convergence of such iterative process to some limit function. Our analysis is based on some conditions on the contractivity of the associated scheme for the differences. In particular, we show the regularity of the limit function, in Lp and Sobolev spaces.

Keywords: non-linear subdivision scheme, convergence of subdivision schemes, box splines

DOI: 10.3233/ASY-2011-1052

Journal: Asymptotic Analysis, vol. 74, no. 3-4, pp. 229-247, 2011