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| 一类四次有理插值样条的点控制 | |
| 引用本文： | 刘植,肖凯,江平,谢进.一类四次有理插值样条的点控制[J].计算数学,2016,38(1):56-64. |
| 作者姓名： | 刘植 肖凯 江平 谢进 |
| 作者单位： | 1. 合肥工业大学数学学院, 合肥 230009; 2. 合肥学院科学计算研究所, 合肥 230601 |
| 基金项目： | 国家自然科学基金，高等学校博士学科点专项科研基金资助课题，安徽省教育厅自然科学重大研究项目，中央高校基本科研业务费专项经费 |
| 摘 要： | 构造了一种有理四次插值样条,其分子为四次多项式分母为二次多项式.该有理插值样条是有界的、保单调且C~2连续的,仅带有一个调节参数δ_i.研究了有理四次插值样条的性质,同时给出了相应的函数值控制、导数值控制方法,这种方法的优点在于能够根据实际设计需要简单地选取适宜的参数,达到对曲线的形状进行局部调控的目的. |
| 关 键 词： | 有理插值样条 四次样条 函数值控制 导数值控制 |
| 收稿时间： | 2014-11-21; |
POINT CONTROL OF RATIONAL QUARTIC INTERPOLATING SPLINE |
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| Liu Zhi,Xiao Kai,Jiang Ping,Xie Jin.POINT CONTROL OF RATIONAL QUARTIC INTERPOLATING SPLINE[J].Mathematica Numerica Sinica,2016,38(1):56-64. | |
| Authors: | Liu Zhi Xiao Kai Jiang Ping Xie Jin |
| Institution: | 1. School of Mathematics, Hefei University of Technology, Hefei 230009, China; 2. Institute of Scientific Computing, Hefei University, Hefei 230601, China |
| Abstract: | A new rational quartic interpolating spline based on derivative values with quadratic denominators are constructed. The monotonicity-preserving and C2 continuity of rational quartic interpolating curves can be confirmed. The rational interpolating spline has simple and explicit representation with parameters δ#em/em#. The function value control and derivative value control methods of the rational quartic interpolating curves are given respectively. The advantage of these control methods is that they can be applied to modifying the local shape of an interpolating curve by simple selecting suitable parameters according to the practical design requirements. |
| Keywords: | rational interpolation spline quartic spline function value control derivative value control |
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