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A family of C2 four-point stationary subdivision schemes with fourth-order accuracy and shape-preserving properties

Title
A family of C2 four-point stationary subdivision schemes with fourth-order accuracy and shape-preserving properties
Authors
YangHyoseonKimKyungmiYoonJungho
Ewha Authors
윤정호
SCOPUS Author ID
윤정호scopus
Issue Date
2024
Journal Title
Journal of Computational and Applied Mathematics
ISSN
0377-0427JCR Link
Citation
Journal of Computational and Applied Mathematics vol. 446
Keywords
Approximation orderCubic B-splineFour-point schemeShape-preservationSmoothnessSubdivision
Publisher
Elsevier B.V.
Indexed
SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
The four-point interpolatory scheme and the cubic B-spline are examples of the most well-known stationary subdivision procedures. They are based on the space of cubic polynomials and have their respective strengths and weaknesses. In this regard, the purpose of this study is to introduce a new type of subdivision scheme that integrates the advantages of both the four-point and the cubic B-spline schemes. The proposed scheme achieves approximation order ‘four’ and an improved smoothness C2, while keeping the same support of the basic limit function as the four-point scheme. Moreover, under some mild conditions, the new scheme has the properties of monotonicity and convexity preservation. Whereas most high-order shape-preserving schemes are non-linear and rather computationally complicated, the proposed scheme is linear and stationary. Several numerical examples are provided to illustrate the efficiency of our subdivision algorithm. © 2024 Elsevier B.V.
DOI
10.1016/j.cam.2024.115843
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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