构造切触有理插值函数的一种新方法  

A new method of constructing osculatory rational interpolating function

作　　者：孙梅兰[1] 丁芳清[1] 

机构地区：[1]合肥学院数理系,安徽合肥230022

出　　处：《合肥工业大学学报（自然科学版）》2012年第5期716-720,共5页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省教育厅自然科学研究资助项目(KJ2010B182);合肥学院自然科学研究发展基金重点资助项目(12KY02ZD)

摘　　要：文章首先将插值节点进行分块,对每块节点作Hermite插值多项式,并利用其剩下的节点作最高次项系数为1的代数多项式;其次对分块Hermite插值多项式及相应的代数多项式,采用线性组合方法得到一般切触有理插值函数的表达式;最后通过引入参数方法,给出设定次数类型的切触有理插值问题有解的条件。实例表明所给方法直观、灵活。Firstly,the interpolating nodes are sliced into blocks and Hermite interpolating polynomial is constructed respectively for each block.For the remaining nodes,the algebraic polynomials are constructed in which the coefficient of the highest order terms is unit.Secondly,the expression of osculatory rational interpolating function is obtained by the linear combination of the blocks of Hermite interpolating polynomials and the corresponding algebraic polynomials.Finally,by using the parameter method,the condition of osculatory rational interpolating problem being solvable is given.Examples show that the given method is intuitive and flexible.

关 键 词：切触有理插值 存在唯一性 参数方法 重差商 

分 类 号：O241.5[理学—计算数学]