| 关于Newton—Thiele型二元有理插值的存在性问题 |
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| 引用本文： | 赵春霞,顾传青.关于Newton—Thiele型二元有理插值的存在性问题[J].应用数学与计算数学学报,2001,15(2):15-22. |
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| 作者姓名： | 赵春霞 顾传青 |
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| 作者单位： | 上海大学数学系,上海,200436 |
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| 基金项目： | 国家自然科学基金资助项目(19871054). |
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| 摘 要： | 基于均差的牛顿插值多项式可以递归地实现对待插值函数的多项式逼近，而Thiele型插值连分式可以构造给定节点上的有理函数。将两者结合可以得到Newton-Thiele型二元有理插值（NTRI）算法，本文解决了NTRI算法的存在性问题，并有数值例子加以说明。
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| 关 键 词： | 均差 二元有理插值 存在性 牛顿插值多项式 NTRI算法 逼近函数 Thiele型插值连分式 |
| 修稿时间： | 2001年4月6日 |
About the Existence of Newton-Thiele's Bivariate Rational Interpolating |
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| ZHAO CHUNXIA GU CHUANQING.About the Existence of Newton-Thiele''''s Bivariate Rational Interpolating[J].Communication on Applied Mathematics and Computation,2001,15(2):15-22. |
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| Authors: | ZHAO CHUNXIA GU CHUANQING |
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| Abstract: | It is well known that Newton's interpolation polynomial is based on divided differences which produce useful intermediate results and allow one to compute the polynomial recursively. Thiele's interpolating continued fraction is aimed at building a rational function which interpolates the given support points. Compounding them we can get NTRI algorithm. In this paper we discuss the existence of NTRI algorithm. A numerical example illustrates the result. |
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| Keywords: | NTRI interpolation |
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