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October, 2020 A Non-stationary Combined Ternary 5-point Subdivision Scheme with $C^{4}$ Continuity
Zeze Zhang, Hongchan Zheng, Weijie Song, Baoxing Zhang
Taiwanese J. Math. 24(5): 1259-1281 (October, 2020). DOI: 10.11650/tjm/200303


In this paper, a family of non-stationary combined ternary $5$-point subdivision schemes with multiple variable parameters is proposed. The construction of the scheme is based on the generalized ternary subdivision scheme of order $4$, which is built upon refinement of a family of generalized B-splines, using the variable displacements. For such a non-stationary scheme, we study its smoothness and get that it can generate $C^{2}$ interpolating limit curves and $C^{4}$ approximating limit curves. Besides, we investigate the exponential polynomial generation/reproduction property and approximation order. It can generate/reproduce certain exponential polynomials with suitable choices of the variable parameters, and reach approximation order $5$.


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Zeze Zhang. Hongchan Zheng. Weijie Song. Baoxing Zhang. "A Non-stationary Combined Ternary 5-point Subdivision Scheme with $C^{4}$ Continuity." Taiwanese J. Math. 24 (5) 1259 - 1281, October, 2020.


Received: 7 July 2019; Revised: 24 December 2019; Accepted: 13 March 2020; Published: October, 2020
First available in Project Euclid: 24 March 2020

MathSciNet: MR4152666
Digital Object Identifier: 10.11650/tjm/200303

Primary: 26A18 , 39B12 , 65D17

Keywords: approximation order , combined scheme , convergence , exponential polynomial generation/reproduction , ternary non-stationary subdivision

Rights: Copyright © 2020 The Mathematical Society of the Republic of China


Vol.24 • No. 5 • October, 2020
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