Smoothness of Nonlinear and Non-Separable Subdivision Schemes

Basarab Matei (1) , Sylvain Meignen (2) , Anastasia Zakharova (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

We study in this paper nonlinear 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 $L^p$ and Sobolev spaces.

Mots clés: Nonlinear subdivision scheme; convergence of subdivision schemes; box splines

Domaines: Analyse numérique [math.NA]

Basarab Matei, Sylvain Meignen, Anastasia Zakharova. Smoothness of Nonlinear and Non-Separable Subdivision Schemes. Asymptotic Analysis, 2011, 74 (3-4), pp.229-247. ⟨10.3233/ASY-2011-1052⟩. ⟨hal-00452897⟩