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
Articolo in rivista - Articolo scientifico
Uniform univariate subdivision; Interpolation; Approximation; Generating function; Link Polynomial Factorization (LPF)
English
2010
216
4
1169
1180
none
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/16128
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