| 关于二元Hermite插值问题的某些研究 |
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| 引用本文： | 崔利宏,徐艳,张双喜,李冕.关于二元Hermite插值问题的某些研究[J].辽宁师范大学学报(自然科学版),2006,29(3):264-266. |
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| 作者姓名： | 崔利宏 徐艳 张双喜 李冕 |
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| 作者单位： | 辽宁师范大学,数学学院,辽宁,大连,116029 |
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| 摘 要： | 主要研究了二维欧氏空间中的Hermite插值问题．我们提出了沿平面代数曲线的Hermite插值唯一可解集和强H-基的基本概念,给出了二维欧氏空间中及沿平面代数曲线上的Hermite插值唯一可解集的相关理论及一般性构造方法，所得结论推广了H．A．Hakoplan,B．Borislar和Yuan Xu等人在2002年及2003年得到的有关单位圆盘上的Hermite插值的主要结果，从而搞清了二元Hermite插值唯一可解集的几何结构和基本特征．
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| 关 键 词： | 二元Hermite插值 沿平面代数曲线的Hermite插值 二元Hermite插值唯一可解集 |
| 文章编号： | 1000-1735(2006)03-0264-03 |
| 收稿时间： | 05 25 2006 12:00AM |
| 修稿时间： | 2006年5月25日 |
Some Researches of Bivariate Hermite Interpolation |
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| CUI Li-hong,XU Yan,ZHANG Shuang-xi,LI Mian.Some Researches of Bivariate Hermite Interpolation[J].Journal of Liaoning Normal University(Natural Science Edition),2006,29(3):264-266. |
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| Authors: | CUI Li-hong XU Yan ZHANG Shuang-xi LI Mian |
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| Institution: | School of Mathematics, Liaoning Normal University, Dalian 116029, China |
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| Abstract: | In this paper, some problems on bivariate Hermite interpolation by polynomial are studied. The concepts of strong H-basis and Hermite interpolation along a plane algebraic curve are proposed. As a result, the general methods for constructing the uniso!vent set for bivariate Hermite interpolation in R^2 and along a plane algebraic curve are deduced, respectively. This generalizes the main resuits acquired by H.A. Hakopian, Borislar Bojanov and Xu Yuan in 2002 and 2003, respectively. |
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| Keywords: | bivariate Hermite interpolation Hermite interpolation along a plane algebraic curve unisolvent set of bivariate Hermite interpolation |
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