高阶导数切触有理插值算法  

An Algorithm of Osculatory Rational Interpolation for High Order Derivative

作　　者：荆科[1,2] 刘业政[1] 康宁[1] 

机构地区：[1]合肥工业大学管理学院,安徽合肥230009 [2]阜阳师范学院数学与统计学院,安徽阜阳236037

出　　处：《应用数学》2015年第4期737-742,共6页Mathematica Applicata

基　　金：国家重点基础研究发展计划(973计划2013CB329603);安徽省高等学校自然科学研究项目(2014FSKJ11)

摘　　要：已有关于高阶导数有理插值方法的研究大都是基于广义范德蒙逆矩阵的思想,计算复杂度较高.本文利用埃米特插值基函数的方法和多项式插值的误差性质,给出一种满足高阶导数插值条件的切触有理插值算法,并且适用于向量值切触有理插值及插值重度不相等的情形,解决切触有理插值函数的存在性及算法复杂性问题.较之其他算法,具有计算复杂度较低,便于实际应用等特点.最后通过数值例子说明该算法的有效性.The current studios of rational interpolation method of higher derivative are mostly based on the idea of generalized Vandermonde inverse matrix, and the complexity of computation is higher. By using of basis function of Hermite interpolation and nature of polynomial interpolation error, we present an algorithm of osculatory rational interpolation which satisfies the condition of higher derivative. In addition it also satisfies the vector-valued osculatory rational interpolation and case of different si. It solvcs the problem of existence of osculatory rational interpolation function and complexity of algorithm. Compared with other algorithms, the complexity of computation is lower, and it is easy to facilitate the practical application, etc. In the end, we illustrate effectiveness of the algorithm by using numerical example.

关 键 词：切触有理插值 误差估计 高阶导数 埃米特插值 

分 类 号：O174.2[理学—数学]