| 平面代数曲线的二元多项式插值问题 |
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| 引用本文： | 崔利宏,杨一浓,王晓婉.平面代数曲线的二元多项式插值问题[J].辽宁师范大学学报(自然科学版),2013(3):318-322. |
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| 作者姓名： | 崔利宏 杨一浓 王晓婉 |
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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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| 基金项目： | 国家自然科学基金项目（41171137） |
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| 摘 要： | 对二元多项式插值问题进行了研究与探讨,并把这个插值问题转化为代数几何问题.通过引进H-基的概念并使用代数几何中的基本定理,得到利用两个任意次代数曲线横截相交的方法来构造平面代数曲线的插值适定结点组的新方法,从而将以往该研究方向所得结果推广到了一般情形.在得到这些研究结果的同时,我们搞清了二元多项式插值适定结点组的几何结构和基本特征,为多元多项式插值在工业产品外形设计和有限元法中的实际应用提供了理论依据.
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| 关 键 词： | 适定结点组 代数曲线 H-基 二元多项式插值 |
Bivariate polynomial interpolation on algebraic curves |
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| CUI Lihong,YANG Yinong,WANG Xiaowan.Bivariate polynomial interpolation on algebraic curves[J].Journal of Liaoning Normal University(Natural Science Edition),2013(3):318-322. |
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| Authors: | CUI Lihong YANG Yinong WANG Xiaowan |
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| Institution: | (School of Mathematics, Liaoning Normal University, Dalian 116029, China) |
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| Abstract: | Through the use of the concept of H-bases we, gets a new method which use the transverse intersection of two algebraic curves to construct the Properly Posed Set of Nodes on a plane curve. Thus we generalizes the obtained results in this field to the most general case, gets a further under- standing of bivariate interpolation for the Properly Posed Set of Nodes geometry construction and es- sential characteristics, and provides the theory basis for the practical application of the polynomial in- terpolation in manufactures industrial products design and finite element. |
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| Keywords: | properly posed set of nodes algebraic curve H-bases bivariate polynomial interpolation |
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