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A non-uniform corner-cutting subdivision scheme with an improved accuracy

Title
A non-uniform corner-cutting subdivision scheme with an improved accuracy
Authors
Jeong B.Yang H.Yoon J.
Ewha Authors
윤정호정병선
SCOPUS Author ID
윤정호scopus; 정병선scopus
Issue Date
2021
Journal Title
Journal of Computational and Applied Mathematics
ISSN
0377-0427JCR Link
Citation
Journal of Computational and Applied Mathematics vol. 391
Keywords
Approximation orderCorner-cutting schemeExponential B-splineNon-uniform subdivision
Publisher
Elsevier B.V.
Indexed
SCIE; SCOPUS scopus
Document Type
Article
Abstract
The aim of this paper is to construct a new non-uniform corner-cutting (NUCC) subdivision scheme that improves the accuracy of the classical (stationary and non-stationary) methods. The refinement rules are formulated via the reproducing property of exponential polynomials. An exponential polynomial has a shape parameter so that it may be adapted to the characteristic of the given data. In this study, we propose a method of selecting the shape parameter, so that it enables the associated scheme to achieve an improved approximation order (that is, three), in case that either the initial data or its derivative is bounded away from zero. In contrast, the classical methods attain the second-order accuracy. An analysis of convergence and smoothness of the proposed scheme is conducted. The proposed scheme is shown to have the same smoothness as the classical Chaikin's corner-cutting algorithm, that is, C1. Finally, some numerical examples are presented to demonstrate the advantages of the new corner-cutting algorithm. © 2021 Elsevier B.V.
DOI
10.1016/j.cam.2021.113446
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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