李昌文,朱晓临,邹乐.修正的 Thiele-Werner型有理插值[J].数学研究及应用,2010,30(4):653~663
修正的 Thiele-Werner型有理插值
Modified Thiele-Werner Rational Interpolation
投稿时间:2008-04-16  最后修改时间:2009-06-30
DOI:10.3770/j.issn:1000-341X.2010.04.010
中文关键词:  插值  修正的Thiele-Werner算法  不可达点.
英文关键词:interpolation  modified Thiele-Werner algorithm  unattainable point.
基金项目:国家自然科学基金(Grant No.60473114),安徽省自然科学基金(Grant No.070416227).
作者单位
李昌文 淮北师范大学数学系, 安徽 淮北 235000; 合肥工业大学数学系, 安徽 合肥 230009 
朱晓临 淮北师范大学数学系, 安徽 淮北 235000 
邹乐 淮北师范大学数学系, 安徽 淮北 235000 
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中文摘要:
      通过插值结点次序的调整,给出了一种修正的 Thiele-Werner型有理插值.这种插值方法不仅避免了在构造 Thiele型连分式插值中逆元素为 $\infty $的情况,而且使得Thiele-Werner型有理插值中的插值多项式为常数,给计算带来方便.本文同时考虑了这种插值的存在性和行列式表达,并将其推广到二元情形,数值例子也说明其有效性.
英文摘要:
      Through adjusting the order of interpolation nodes, we gave a kind of modified Thiele-Werner rational interpolation. This interpolation method not only avoids the infinite value of inverse differences in constructing the Thiele continued fraction interpolation, but also simplifies the interpolating polynomial coefficients with constant coefficients in the Thiele-Werner rational interpolation. Unattainable points and determinantal expression for this interpolation are considered. As an extension, some bivariate analogy is also discussed and numerical examples are given to show the validness of this method.
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