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二元向量值有理插值的一种递推算法
引用本文:闵杰,朱功勤,刘智秉.二元向量值有理插值的一种递推算法[J].合肥工业大学学报(自然科学版),2004,27(6):623-626.
作者姓名:闵杰  朱功勤  刘智秉
作者单位:合肥工业大学,理学院,安徽,合肥,230009
摘    要:一般二元向量值有理插值的算法多利用分叉连分式的方法。文章利用插值型值点复数化的方法讨论并给出了二元向量值有理插值的一种新算法,即把平面上的插值结点视为一个复数,所对应的向量视为一个复向量,使用一元Thiele型向量值有理插值公式的构造方法和向量连分式的向后三项递推关系式以及适当的变换,最后导出了这种递推算法。所得算法避免了使用分叉连分式,具有更大的有效性和灵活性。

关 键 词:复数化  向量值有理插值  三项递推关系式  算法
文章编号:1003-5060(2004)06-0623-04
修稿时间:2003年5月7日

A recursive algorithm of bivariate vector valued rational interpolants
MIN Jie,ZHU Gong-qin,LIU Zhi-bing.A recursive algorithm of bivariate vector valued rational interpolants[J].Journal of Hefei University of Technology(Natural Science),2004,27(6):623-626.
Authors:MIN Jie  ZHU Gong-qin  LIU Zhi-bing
Abstract:The method of branched continued fractions has been commonly used in the algorithm of bivariate vector valued rational interpolants.In this paper,a new algorithm is given by means of the complexification of the knots,i.e. the node in the plane is considered as a complex point,the vector as a complex vector,and then based on the construction of vector valued Thiele type rational interpolants and the backward three-term recurrence relation for vector valued continued fractions,the recursive algorithm is obtained by appropriate transformation.This algorithm has more validity and flexibility for the using of branched continued fractions is avoided .
Keywords:complexification  vector valued rational interpolant  three-term recurrence relation  algorithm
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