一类具有优良性质的五点二重逼近细分格式

doi:10.12341/jssms13273

系统科学与数学 ›› 2017, Vol. 37 ›› Issue (10): 2155-2162.DOI: 10.12341/jssms13273

• 论文 • 上一篇

一类具有优良性质的五点二重逼近细分格式

王燕¹，李志明²

1. 合肥师范学院数学与统计学院,合肥 230601;2. 合肥工业大学计算机与信息学院,合肥 230009

出版日期:2017-10-25 发布日期:2017-12-14

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王燕，李志明. 一类具有优良性质的五点二重逼近细分格式[J]. 系统科学与数学, 2017, 37(10): 2155-2162.

WANG Yan, LI Zhiming. A Five-Point Binary Approximating Subdivision Scheme with Good Properties[J]. Journal of Systems Science and Mathematical Sciences, 2017, 37(10): 2155-2162.

A Five-Point Binary Approximating Subdivision Scheme with Good Properties

WANG Yan¹ , LI Zhiming²

1.School of Mathematics and Statistics, Hefei Normal University, Hefei 230601; 2.School of Computer and Information, Hefei University of Technology, Hefei 230009

Online:2017-10-25 Published:2017-12-14

提出了一类带两个形状参数的五点二重逼近细分格式.这类格式具有一些优良的性质:高阶连续性、可调性和多项式再生性质.对于参数的某些取值范围极限曲线可以达到$C^k~(k=0,1,\cdots,7)$ 连续,分析了一类特殊情况的多项式再生性质.实例表明该格式的有效性和灵活性.

关键词： 二重细分, 收敛性和光滑性, 多项式再生.

A new five-point binary approximating subdivision scheme with two parameters is proposed in this paper. The scheme has some good properties, such as high continuity, flexibility and polynomial reproduction property. It is shown that the limiting curves are $C^k~(k=0,1,\cdots,7)$ continuous for certain ranges of the parameters. Polynomial reproduction property is also analyzed for a special case. Experimental results demonstrate the efficiency and flexibility of the scheme.

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