平面代数曲线上Birkhoff插值问题研究  

Research on the Birkhoff Interpolation Problem on Plane Algebraic Curves

作　　者：徐照强 谭雅文 崔利宏[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《应用数学进展》2025年第1期98-104,共7页Advances in Applied Mathematics

摘　　要：本文以一元Birkhoff插值研究结果为基础,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Gröbner基的概念及其发现其性质,提出了一种利用两条不同次数代数曲线相交的点,构造出二元Birkhoff插值问题适定泛函组的新方法,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,最后给出了具体实验算例,对所得研究结论给予了验证。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 Gröbner 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’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.

关 键 词：BIRKHOFF插值 平面代数曲线 插值适定泛函组 

分 类 号：O31[理学—一般力学与力学基础]