Multiple subdivision schemes

Authors:
Tomas Sauer
Affiliations:
Lehrstuhl für Numerische Mathematik, Justus---Liebig---Universität Gießen, Gießen, Germany
Venue:
Proceedings of the 7th international conference on Curves and Surfaces
Year:
2010

Citing 5
Cited 0

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Abstract

Motivated by the concept of directionally adapted subdivision for the definition of shearlet multiresolution, the paper considers a generalized class of multivariate stationary subdivision schemes, where in each iteration step a scheme and a dilation matrix can be chosen from a given finite set. The standard questions of convergence and refinability will be answered as well as the continuous dependence of the resulting limit functions from the selection process. In addition, the concept of a canonical factor for multivariate subdivision schemes is introduced, which follows in a straightforward fashion from algebraic properties of the scaling matrix and takes the role of a smoothing factor for symbols.