一次有理插值样条  

Linear rational spline interpolation

作　　者：唐如忠[1] 赵前进[1] 张玉武[1] 

机构地区：[1]安徽理工大学理学院,淮南232001

出　　处：《安徽建筑工业学院学报（自然科学版）》2010年第1期76-78,82,共4页Journal of Anhui Institute of Architecture(Natural Science)

基　　金：国家自然科学基金(60973050;30570431;60873144);安徽省教育厅自然科学基金项目(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项目基金(2006AA01Z104)资助

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。首先基于给定的权构造的重心有理插值来计算导数的近似值,通过适当选择形状参数,插值函数一阶连续且保单调来构造1/1型有理插值样条,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。It is well known that barycentric rational interpolation have sufficiently smooth,no poles and high approximation orders,regardless of the distribution of the points.Firstly,given weights based local barycentric rational interpolants are constructed and the approximate values of derivatives are obtained.Secondly,new rational interpolation spline with linear numerator and linea denominator is presented.The sheme has been used to obtain a C1 curve and at the same times preserves monotonicity.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：O174.41[理学—数学]