In this paper we show that the refinement rules of interpolating and approximating univariate subdivision schemes with odd-width masks of finite support can be derived ones from the others by simple operations on the mask coefficients. These operations are formalized as multiplication/division of the associated generating functions by a proper link polynomial. We then apply the proposed result to some families of stationary and non-stationary subdivision schemes, showing that it also provides a constructive method for the definition of novel refinement algorithms
Beccari, C., Casciola, G., Romani, L. (2010). A unified framework for interpolating and approximating univariate subdivision. APPLIED MATHEMATICS AND COMPUTATION, 216(4), 1169-1180 [10.1016/j.amc.2010.02.009].
A unified framework for interpolating and approximating univariate subdivision
ROMANI, LUCIA
2010
Abstract
In this paper we show that the refinement rules of interpolating and approximating univariate subdivision schemes with odd-width masks of finite support can be derived ones from the others by simple operations on the mask coefficients. These operations are formalized as multiplication/division of the associated generating functions by a proper link polynomial. We then apply the proposed result to some families of stationary and non-stationary subdivision schemes, showing that it also provides a constructive method for the definition of novel refinement algorithms
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