关于切触有理插值问题的一种分段方法  

Slicing method of constructing osculatory rational interpolating function

作　　者：孙梅兰[1] 朱功勤[2] 谢进[1] 

机构地区：[1]合肥学院数学与物理系,合肥230601 [2]合肥工业大学计算机与信息学院,合肥230009

出　　处：《计算机工程与应用》2012年第7期60-63,共4页Computer Engineering and Applications

基　　金：国家自然科学基金(No.11026076;60473114);安徽省教育厅自然科研基金项目(No.KJ2010B182);安徽省教育厅高校优秀青年人才基金资助项目(No.2009SQRZ158);合肥学院科学发展基金重点项目(No.12KY02ZD)

摘　　要：将插值节点进行分段,利用分段Hermite插值多项式及相应的多项式,采用线性组合方法得到一般切触有理插值函数的表达式,还可方便地给出无极点的切触有理插值函数的构造方法。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,证明了解的存在唯一性,并给出误差估计公式。实例表明所给方法具有直观、灵活和有效性,便于实际应用。The interpolating nodes are sliced and Hermite interpolating polynomial is constructed respectively in this paper. Algebra polynomials which coefficient of the highest order terms is unit are constructed with the remaining nodes. The rational function expression satisfying interpolating conditions is obtained with linear combination method. By introducing parameters, it proves that the osculatory rational interpolation function is existent and unique. And the error estimation formula is produced. Examples show that the proposed mothod is intuitive, flexible, efficient and easy to facilitate to practical application with smaller volume of the calculation.

关 键 词：切触有理插值 存在唯一性 分段方法 重差商 

分 类 号：O241.5[理学—计算数学]