矩形网格上的Thiele重心型连分式混合有理插值  

THIELE-BARYCENTRIC TYPE BLENDING RATIONAL INTERPOLANTS BY CONTINUED FRACTIONS OVER RECTANGULAR GRIDS

作　　者：唐烁[1] 余小磊[1] 赵欢喜[2] 

机构地区：[1]合肥工业大学数学学院,合肥230009 [2]中南大学信息科学与工程学院,长沙410083

出　　处：《高等学校计算数学学报》2013年第1期40-48,共9页Numerical Mathematics A Journal of Chinese Universities

基　　金：Supported by the National Natural Science Foundation of China(No.61272024;60473114);the Key Project Foundation of Education Department of Anhui Province(No.KJ2008A027)

摘　　要：众所周知，有理插值是非线性逼近的一种重要方法，但由于其复杂性，主要表现在有理插值问题有解是有条件的或者说有理插值问题不是总是有解的．熟知的有理插值格式（包括向量有理插值、矩阵有理插值）函数构造方法，都是假定有理插值问题有解的条件下给出的，为实际应用带来一定的困难．Laid foundation on the advantages of the simple expressions, easy to calculate of continued fractions and small calculation quantity, no poles, good numerical stability of barycentric rational interpolants, bivariate blending rational interpolation are constructed based on Thiele-type continued fraction interpolation and Barycentric rational interpolants. The new blending rational interpolation inherits the advantages of the continued fraction interpolation and the barycentric interpolats, and the error estimation is given. Numerical example is given to show the correctness and effectiveness of the new method.

关 键 词：向量有理插值 矩形网格 连分式 有理插值问题 混合 重心 非线性逼近 插值格式 

分 类 号：O241.5[理学—计算数学]