切触有理插值函数的新算法  

A NEW ALGORITHM OF OSCULATORY RATIONAL INTERPOLATION FUNCTION

作　　者：荆科[1,2] 康宁[3] 

机构地区：[1]合肥工业大学管理学院,合肥230009 [2]阜阳师范学院数学与计算科学学院,阜阳236037 [3]阜阳师范学院经济与管理学院,阜阳236037

出　　处：《系统科学与数学》2014年第2期238-244,共7页Journal of Systems Science and Mathematical Sciences

基　　金：973计划(2013CB329603);国家特色专业数学与应用数学(TS11496);阜阳师范学院自然科学基金(2013FSKJ11)资助课题

摘　　要：切触有理插值函数的算法大都是基于连分式进行的,其算法的可行性大都是有条件的,且有理函数次数较高,计算量较大.文章利用拉格朗日插值的性质和分段组合的方法,给出了一种新的切触有理插值算法,并给出误差估计且将其推广到向量值切触有理插值情形.较之其他算法,具有有理函数次数较低、计算量较小、算法无条件性、无极点、满足高阶导数插值条件等优点.The algorithms of constructing osculatory rational interpolation are mostly based on the continued fraction.Feasibility of the algorithm is conditional,the de gree of rational function is high and the computation is large.We give an algorithm of osculatory rational interpolation function and error estimates,and extend it to vector-valued case.Compared to other algorithms,the degree of rational function is lower.It needs less computation,feasibility of the algorithm is unconditional,and it has no real poles and meets the condition of higher order derivative interpolation condition.

关 键 词：切触有理插值 分段组合方法 插值公式 埃米特插值 

分 类 号：O241.3[理学—计算数学]