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Analysis of stationary subdivision schemes for curve design based on radial basis function interpolation

Title
Analysis of stationary subdivision schemes for curve design based on radial basis function interpolation
Authors
Lee Y.J.Yoon J.
Ewha Authors
윤정호
SCOPUS Author ID
윤정호scopus
Issue Date
2010
Journal Title
Applied Mathematics and Computation
ISSN
0096-3003JCR Link
Citation
vol. 215, no. 11, pp. 3851 - 3859
Indexed
SCIE; SCOPUS WOS scopus
Abstract
This paper provides a large family of interpolatory stationary subdivision schemes based on radial basis functions (RBFs) which are positive definite or conditionally positive definite. A radial basis function considered in this study has a tension parameter λ > 0 such that it provides design flexibility. We prove that for a sufficiently large λ ≥ λ0, the proposed 2 L-point (L ∈ N) scheme has the same smoothness as the well-known 2 L-point Deslauriers-Dubuc scheme, which is based on 2 L - 1 degree polynomial interpolation. Some numerical examples are presented to illustrate the performance of the new schemes, adapting subdivision rules on bounded intervals in a way of keeping the same smoothness and accuracy of the pre-existing schemes on R. We observe that, with proper tension parameters, the new scheme can alleviate undesirable artifacts near boundaries, which usually appear to interpolatory schemes with irregularly distributed control points. © 2009 Elsevier Inc. All rights reserved.
DOI
10.1016/j.amc.2009.11.028
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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