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一类带参数的有理三次三角Hermite插值样条

谢进1,2, 檀结庆2, 刘植2, 李声锋3   

  1. 1. 合肥学院 数学与物理系 合肥 230601;
    2. 合肥工业大学 计算机与信息学院 合肥 230009;
    3. 蚌埠学院 数学与物理系 安徽蚌埠 233000
  • 收稿日期:2009-08-11 出版日期:2011-05-15 发布日期:2011-06-04
  • 基金资助:

    国家自然科学基金资助项目(61070227);教育部科学技术研究重大项目(309017);教育部博士点基金(20070359014); 安徽省教育厅教研重点项目(20100935);合肥学院科研重点项目(11KY02ZD).

谢进, 檀结庆, 刘植, 李声锋. 一类带参数的有理三次三角Hermite插值样条[J]. 计算数学, 2011, 33(2): 125-132.

Xie Jin, Tan Jieqing, Liu Zhi, Li Shengfeng. A CLASS OF RATIONAL CUBIC TRIGONOMETRIC HERMITE INTERPOLATING SPLINES WITH PARAMETERS[J]. Mathematica Numerica Sinica, 2011, 33(2): 125-132.

A CLASS OF RATIONAL CUBIC TRIGONOMETRIC HERMITE INTERPOLATING SPLINES WITH PARAMETERS

Xie Jin1,2, Tan Jieqing2, Liu Zhi2, Li Shengfeng3   

  1. 1. Department of Mathematics and Physics, Hefei University, Hefei 230601, China;
    2. School of Computer & Information, Hefei University of Technology, Hefei 230009, China;
    3. Department of Mathematics and Physics, Bengbu College, Bengbu 233000, Anhui, China
  • Received:2009-08-11 Online:2011-05-15 Published:2011-06-04

给出一种带有参数的有理三次三角Hermite插值样条, 具有标准三次Hermite插值样条相似的性质. 利用参数的不同取值不但可以调控插值曲线的形状, 而且比标准三次Hermite插值样条更好地逼近被插曲线. 此外, 选择合适的控制点, 该种插值样条可以精确表示星形线和四叶玫瑰线等超越曲线.

A class of rational cubic trigonometric Hermite interpolating splines with parameters is presented in this paper, which shares the same properties of standard cubic Hermite interpolating splines. The shape of the interpolation curves not only can be adjusted, but also more approximates the interpolated curves than standard cubic Hermite interpolating splines with taking different values of parameters. Moreover, by selecting proper control points, the spline curves can represent transcendantal curves exactly, such as tetracuspid and quadrifolium.

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