Regularity of non-stationary subdivision: a matrix approach

Numer Math (Heidelb). 2017;135(3):639-678. doi: 10.1007/s00211-016-0809-y. Epub 2016 May 12.

Abstract

In this paper, we study scalar multivariate non-stationary subdivision schemes with integer dilation matrix M and present a unifying, general approach for checking their convergence and for determining their Hölder regularity (latter in the case [Formula: see text]). The combination of the concepts of asymptotic similarity and approximate sum rules allows us to link stationary and non-stationary settings and to employ recent advances in methods for exact computation of the joint spectral radius. As an application, we prove a recent conjecture by Dyn et al. on the Hölder regularity of the generalized Daubechies wavelets. We illustrate our results with several examples.

Keywords: 15A60; 39A99; 65D17.