矩形网格上的二元切触有理插值

荆科; 康宁

doi:10.3879/j.issn.1000-0887.2015.06.010

矩形网格上的二元切触有理插值

doi: 10.3879/j.issn.1000-0887.2015.06.010

荆科^1,2,
康宁³

¹阜阳师范学院数学与金融学院,安徽阜阳 236037;²合肥工业大学管理学院,合肥 230009;³阜阳师范学院经济与管理学院,安徽阜阳 236037

基金项目: 国家重点基础研究发展计划（973计划）（2013CB329600）;国家自然科学基金（71371062）;安徽省自然科学基金（1408085MD70）;安徽省高校省级自然科学研究项目(2014KJ011)

详细信息

作者简介:
荆科（1983—），男，安徽颍上人，博士生(E-mail: jingxuefei296@sina.com)；唐宁（1986—），女，安徽利辛人，讲师，博士生(通讯作者. E-mail: kangningning2006@126.com).

中图分类号: O241.3
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- 被引次数: 0
出版历程
- 收稿日期: 2014-09-09
- 修回日期: 2014-10-13
- 刊出日期: 2015-06-15

Bivariate Osculatory Rational Interpolation on Rectangular Grids

JING Ke^1,2,
KANG Ning³

¹School of Mathematics and Finance, Fuyang Teachers College, Fuyang, Anhui 236037, P.R.China;²School of Management, Hefei University of Technology, Hefei 230009, P.R.China;³School of Economics and Management, Fuyang Teachers College, Fuyang, Anhui 236037, P.R.China

Funds: The National Basic Research Program of China (973 Program)（2013CB329600）;The National Natural Science Foundation of China（71371062）

摘要

摘要: 二元切触有理插值是有理插值的一个重要内容，而降低其函数的次数和解决其函数的存在性是有理插值的一个重要问题.二元切触有理插值算法的可行性大都是有条件的，且计算复杂度较大，有理函数的次数较高.利用二元Hermite（埃米特）插值基函数的方法和二元多项式插值误差性质，构造出了一种二元切触有理插值算法并将其推广到向量值情形.较之其它算法，有理插值函数的次数和计算量较低.最后通过数值实例说明该算法的可行性是无条件的，且计算量低.
- 二元切触有理插值 /
- 误差公式 /
- 二元Hermite插值 /
- 基函数
Abstract: The bivariate osculatory rational interpolation is an important element of rational interpolation, and reducing the degrees of the osculatory rational interpolation functions and solving their existence make an important problem. The bivariate osculatory rational interpolation algorithms mostly have conditional feasibility and massive computational complexity with high function degrees. A bivariate osculatory rational interpolation algorithm was obtained on rectangular grids and extended to vector-valued cases, with the method of bivariate Hermite interpolation basis function in view of the error characteristics of bivariate polynomial interpolation. The numerical examples illustrate that, compared to other methods, the feasibility of the presented algorithm is unconditional, the degrees of the related rational functions are lower, and the algorithm has less computational complexity.
- bivariate osculatory rational interpolation /
- error formula /
- bivariate Hermite interpolation /
- basis function

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参考文献(16)

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