TY - JOUR
T1 - Polynomial reproduction by symmetric subdivision schemes
AU - Dyn, Nira
AU - Hormann, Kai
AU - Sabin, Malcolm A.
AU - Shen, Zuowei
N1 - Funding Information:
The fourth author was partially supported under Grant R-146-000-060-112 at the National University of Singapore.
PY - 2008/11
Y1 - 2008/11
N2 - We first present necessary and sufficient conditions for a linear, binary, uniform, and stationary subdivision scheme to have polynomial reproduction of degree d and thus approximation order d + 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.
AB - We first present necessary and sufficient conditions for a linear, binary, uniform, and stationary subdivision scheme to have polynomial reproduction of degree d and thus approximation order d + 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.
KW - Approximation order
KW - Polynomial generation
KW - Polynomial reproduction
KW - Quasi-interpolation.
KW - Subdivision schemes
UR - http://www.scopus.com/inward/record.url?scp=56249096912&partnerID=8YFLogxK
U2 - 10.1016/j.jat.2008.04.008
DO - 10.1016/j.jat.2008.04.008
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AN - SCOPUS:56249096912
VL - 155
SP - 28
EP - 42
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
SN - 0021-9045
IS - 1
ER -