3/1型有理插值样条  

3/1-type rational spline interpolation

作　　者：赵前进[1] 唐如忠[1] 张玉武[1] 

机构地区：[1]安徽理工大学理学院,安徽淮南232001

出　　处：《安徽工程科技学院学报（自然科学版）》2010年第1期65-68,共4页Journal of Anhui University of Technology and Science

基　　金：国家自然科学基金资助项目(60973050;30570431;60873144);安徽省教育厅自然科学基金项目资助(kj2009a50;kj2007b173);安徽省优秀人才基金;教育部新世纪优秀人才支持计划(NCET-06-0555);国家863高技术研究发展计划基金项目资助(2006aa01z104)

摘　　要：重心有理插值在整个插值区间上具有足够的光滑性、不存在极点,且具有很高的逼近阶.首先基于给定权构造的重心有理插值来计算导数的近似值,再通过两族参数作为形状调节参数来构造3/1型有理插值样条使得插值函数保单调,保凸,最后分析了误差并给出了数值例子来说明新方法的有效性.Barycentric rational interpolation have sufficient smoothness, no poles and high approximation orders, regardless of the distribution of the points. Firstly, given weights based on barycentric rational interpolants are constructed and the approximate values of derivatives are obtained. Secondly, new rational interpolation spline with cubic numerator and linear denominator is presented. The sheme has been used to obtain a C1 curve and at the same time preserves monotonicity,convexity. Data dependent shape constraints are derived on two families of parameters to enture preserving the shape of the data while the other two families of parameters are left free for user to control and modify the shape of the given data further in the desired region of curve. Lastly, the error and a numerical example are given to show the effectiveness of the new method.

关 键 词：权 重心有理插值 有理插值样条 保形 

分 类 号：O242[理学—计算数学]