Article ID Journal Published Year Pages File Type
4608086 Journal of Approximation Theory 2008 15 Pages PDF
Abstract

We first present necessary and sufficient conditions for a linear, binary, uniform, and stationary subdivision scheme to have polynomial reproduction of degree dd and thus approximation order d+1d+1. Our conditions are partly algebraic and easy to check by considering the symbol of a subdivision scheme, but also relate to the parameterization of the scheme. After discussing some special properties that hold for symmetric schemes, we then use our conditions to derive the maximum degree of polynomial reproduction for two families of symmetric schemes, the family of pseudo-splines and a new family of dual pseudo-splines.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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