一种关于三元分叉连分式有理插值的新算法  

A New Algrithm of Triple Branched Continuced Fraction Rational Interpolation

作　　者：方艳梅[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《安徽师范大学学报（自然科学版）》2013年第6期531-536,共6页Journal of Anhui Normal University(Natural Science)

摘　　要：在有理函数插值格式的构造方法中,最常用的是基于Thiele型连分式的插值方法,值得注意的是Thiele有理插值与第三种分叉连分式可以利用类似于张量积的方法结合在一起产生一种三元有理插值.本文主要研究三元混合有理插值,通过引入混合差商,构造了三元插值公式,并给出了它的对偶形式,最后用数值例子验证了此算法的有效性.In the method of constructing the rational interpolation,the most commonly method is based on the Thiele continued fraction interpolation.It is interesting to notice that Thiele＇s polynomial interpolation and branched continued fractions interpolation can be incorporated in tensor-product-like manner to build a kind of triple interpolation scheme.This paper mainly studies the triple blending rational interpolation,by introducing the so-called blending partial differences to construct triple interpolation formula,and dual form is given,a numerical example is given to demonstrate the effectiveness of the algorithm at last.

关 键 词：有理插值 分叉连分式 对偶形式 混合差商 

分 类 号：O241.3[理学—计算数学]