| 构造二元向量值有理插值函数的一种新方法 |
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| 引用本文： | 郑林,朱功勤.构造二元向量值有理插值函数的一种新方法[J].数学研究及应用,2011,31(4):605-616. |
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| 作者姓名： | 郑林 朱功勤 |
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| 作者单位： | 上海大学数学系, 上海 200444;合肥工业大学 数学系, 安徽 合肥 230009 |
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| 基金项目： | 上海自然科学基金(Grant No.10ZR1410900), 上海市教委重点项目(Grant No.S30104),安徽省自然科学基金(Grant No.070416227),合肥工业大学学生创新基金(Grant No.XS08079). |
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| 摘 要： | At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 （0 〈 dl ≤ m） and d2 （0 ≤ d2≤ n）, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.
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| 关 键 词： | bivariate vector valued rational interpolation nonnegative integer parameter divide piece primary function interpolation formula. |
| 收稿时间： | 2009/10/17 0:00:00 |
| 修稿时间： | 2011/1/12 0:00:00 |
A New Method of Constructing Bivariate Vector Valued Rational Interpolation Function |
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| Lin ZHENG and Gong Qin ZHU.A New Method of Constructing Bivariate Vector Valued Rational Interpolation Function[J].Journal of Mathematical Research with Applications,2011,31(4):605-616. |
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| Authors: | Lin ZHENG and Gong Qin ZHU |
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| Institution: | 1. Department of Mathematics, Shanghai University, Shanghai, 200444, P.R.China
2. Department of Mathematics, Hefei University of Technology, Anhui, 230009, P.R.China |
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| Abstract: | At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters $ d_{1}~(0\leq d_{1}\leq m)$ and $d_{2}~(0\leq d_{2}\leq n)$, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower. |
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| Keywords: | bivariate vector valued rational interpolation nonnegative integer parameter divide piece primary function interpolation formula |
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