基于Taylor算子的二元向量切触有理插值

经慧芹

doi:10.3879/j.issn.1000-0887.2016.04.008

基于Taylor算子的二元向量切触有理插值

doi: 10.3879/j.issn.1000-0887.2016.04.008

经慧芹

昆明理工大学成人教育学院, 昆明 650051

基金项目: 云南省教育厅科学研究基金重点项目（2015Z043）

详细信息

作者简介:
经慧芹（1966—），女，副教授，硕士（E-mail: kmjhq@163.com）.

中图分类号: O241.3
计量
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- 被引次数: 0
出版历程
- 收稿日期: 2015-11-16
- 修回日期: 2015-12-29
- 刊出日期: 2016-04-15

Bivariate Vector-Valued Osculatory Rational Interpolation Based on the Taylor Operator

JING Hui-qin

Adult Education College, Kunming University of Science and Technology, Kunming 650051, P.R.China

摘要

摘要: 提出了一种基于Taylor算子的二元向量切触有理插值的新方法.首先应用已知的节点定义各阶有理插值基函数，再用相应的向量值和各阶偏导数值建立一种类似二元函数Taylor公式的新型插值算子，最后进行组合运算，得出二元向量一阶、二阶切触有理插值函数的显式表达式，并自然推广到k阶情形，还给出了误差估计.算例表明，该方法计算简单，过程公式化，有应用价值.
- 切触有理插值 /
- 二元向量 /
- Taylor算子 /
- 基函数 /
- 插值函数
Abstract: A new approach based on the Taylor operator was proposed for the bivariate vectorvalued osculatory rational interpolation. First, the rational interpolation basis functions of each order were defined by means of the known nodes. Second, a new type of interpolation operator similar to the Taylor formula for bivariate functions was established with the corresponding vector values and partial derivative values of each order. At last, the combined operations were carried out, and the explicit expressions of the bivariate vectorvalued osculatory rational interpolation functions of the 1st and 2nd orders were obtained. Naturally this approach was generalized to the kth order, and the error estimates were also made. The results of an example show that, this new approach is simple and formularized in calculation, and therefore potential for application.
- osculatory rational interpolation /
- bivariate vector /
- Taylor operator /
- basis function /
- interpolation function

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参考文献(27)

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