一种切触有理插值的构造方法  

A new method of constructing osculatory rational interpolation function

作　　者：荆科[1] 康宁[2] 姚云飞[1] 

机构地区：[1]阜阳师范学院数学与计算科学学院,安徽阜阳236041 [2]阜阳师范学院经济与管理学院,安徽阜阳236041

出　　处：《中国科学技术大学学报》2013年第6期477-479,485,共4页JUSTC

基　　金：国家特色专业(数学与应用数学TS11496);安徽省高等学校省级教学质量与教学改革工程重点项目(20101984);安徽省高校自然科学研究项目(KJ2013Z268);阜阳师范学院科研项目(2012FSKJ07)资助

摘　　要：切触有理插值的构造方法大都是基于连分式进行的,其算法可行性是有条件的,且计算量非常大.利用Hermite插值基函数的方法和多项式插值的误差公式,构造出了切触有理插值函数并将其推广到向量值情形.相比于其他方法,其构造过程公式化,切触有理插值函数次数较低,且计算量较小,便于实际应用.Abstract. The methods for constructing osculatory rational interpolation are mostly based on the continued fraction, but its feasibility of the algorithm is conditional and involves large amounts of computation. The osculatory rational interpolation function was constructed and extended to vector-valued osculatory rational interpolation, by means of the method of Hermite interpolation basis function and the error theory of polynomial interpolation. Compared to other methods, the course of constructing is formulary, the degree of rational function is lower, and the algorithm need less computation and facilitate the practical application.

关 键 词：切触有理插值 误差公式 插值公式 HERMITE插值 

分 类 号：O241.3[理学—计算数学]