| 一类保凸的有理三次插值样条 |
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| 引用本文： | 田萌,李世龙.一类保凸的有理三次插值样条[J].山东大学学报(理学版),2007,42(10):80-83. |
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| 作者姓名： | 田萌 李世龙 |
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| 作者单位： | 1. 山东理工大学,数学与信息科学学院,山东,淄博,255049
2. 山东经济学院,统计与数学学院,山东,济南,250014 |
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| 摘 要： | 利用分段有理三次插值样条解决了凸数据的保形问题. 该插值方法不需要对型值点强加限制,插值曲线可达到C1连续. 实例表明该方法实现了插值曲线保凸, 此外还给出了该样条的逼近性质分析.
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| 关 键 词： | 有理样条 插值 保凸 逼近 |
| 文章编号： | 1671-9352（2007）10-0080-04 |
| 修稿时间： | 2006-09-01 |
Convexity-preserving piecewise rational cubic interpolation |
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| TIAN Meng,LI Shi-long.Convexity-preserving piecewise rational cubic interpolation[J].Journal of Shandong University,2007,42(10):80-83. |
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| Authors: | TIAN Meng LI Shi-long |
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| Institution: | 1. School of Mathematics and Information, Shandong University ofTechnology, Zibo 255049;2. Department of Mathematics and Statis, Shandong Economic University, Jinan 250014, Shandong, China |
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| Abstract: | An explicit representation of a C^1 piecewise rational cubicspline was developed, which can produce a convex interpolant to given convex data. The explicit representation was easily constructed, and no additional restriction on data was needed. Numerical experiments indicate that the method produces visually pleasing curves. Furthermore, an error analysis of the interpolant was given. |
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| Keywords: | rational spline interpolation convexity-preserving approximation |
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