%0 Journal Article
%T 平面代数曲线上Birkhoff插值问题研究<br>Research on the Birkhoff Interpolation Problem on Plane Algebraic Curves
%A 徐照强
%A 谭雅文
%A 崔利宏
%J Advances in Applied Mathematics
%P 98-104
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.141013
%X 本文以一元Birkhoff插值研究结果为基础&#65292;对二元Birkhoff插值泛函组的适定性问题进行了研究。通过提出弱Gr&#246;bner基的概念及其发现其性质&#65292;提出了一种利用两条不同次数代数曲线相交的点&#65292;构造出二元Birkhoff插值问题适定泛函组的新方法&#65292;从而将该方法所得到的结果推广到一般情形。并得到了构造平面代数曲线二元Birkhoff插值适定泛函组的一般性方法和实用性较强的理论&#65292;最后给出了具体实验算例&#65292;对所得研究结论给予了验证。<br>This paper takes the research results of univariate Birkhoff interpolation as its foundation to study the stability problem of two-dimensional Birkhoff interpolation generalized function sets. By introducing the concept and properties of weak Gr&#246;bner bases, a new method is obtained which utilizes the intersection of any two arbitrary algebraic curves to construct the two-dimensional Birkhoff well-posed interpolation functional systems. This method extends the research direction&#8217;s findings to general cases, providing a general approach and practical theory for constructing planar algebraic curve well-posed interpolation functional systems. Finally, specific experimental examples are provided to validate the research conclusions obtained.
%K Birkhoff插值&#65292
%K 平面代数曲线&#65292
%K 插值适定泛函组<br>Birkhoff Interpolation
%K Planar Algebraic Curves
%K Well-Posed Interpolation Functional Systems
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=105377