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https://doi.org/10.1016/j.jat.2008.04.008
Title: | Polynomial reproduction by symmetric subdivision schemes | Authors: | Dyn, N. Hormann, K. Sabin, M.A. Shen, Z. |
Keywords: | Approximation order Polynomial generation Polynomial reproduction Quasi-interpolation. Subdivision schemes |
Issue Date: | Nov-2008 | Citation: | Dyn, N., Hormann, K., Sabin, M.A., Shen, Z. (2008-11). Polynomial reproduction by symmetric subdivision schemes. Journal of Approximation Theory 155 (1) : 28-42. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jat.2008.04.008 | Abstract: | 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. © 2008 Elsevier Inc. All rights reserved. | Source Title: | Journal of Approximation Theory | URI: | http://scholarbank.nus.edu.sg/handle/10635/103946 | ISSN: | 00219045 | DOI: | 10.1016/j.jat.2008.04.008 |
Appears in Collections: | Staff Publications |
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