实多项式函数的退化临界点类型
On types of degenerate critical points of real polynomial functions
摘要：
本文考虑多元多项式函数$f$的退化孤立实临界点$c$的类型（局部极小、极大或鞍点）的判别问题.为此，我们借助于$f$的切线，引入了$c$的忠实半径的定义.证明了$c$的类型可以由以$c$为中心的欧氏球上$f$的全局极值来确定，并给出了计算$c$的忠实半径和确定其类型的算法.
英文摘要：
In this paper, we consider the problem of identifying the type (local minimizer, maximizer or saddle point) of a given isolated real critical point $c$, which is degenerate, of a multivariate polynomial function $f$. To this end, we introduce the definition of faithful radius of $c$ by means of the curve of tangency of $f$. We show that the type of $c$ can be determined by the global extrema of $f$ over the Euclidean ball centered at $c$ with a faithful radius.We propose algorithms to compute a faithful radius of $c$ and determine its type.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
