一个鞍点定理及其应用

A Saddle-point Theorem and Its Application

利用边缘极值点集概念,得到了二元函数f(x,y)有鞍点的充分必要条件,将其推广到矩阵,得到了矩阵存在鞍点的一个充分必要条件,并设计了一个求矩阵所有鞍点的算法。利用该算法,可以求出一个矩阵的所有鞍点,且该算法总的时间复杂度为O(m×n)。

With the concept of edge-extreme-point sets,the necessary and sufficient condition was obtained for the function f(x,y),which has saddle points.At the end,the algorithm,has time complexity of O(m×n),for computing a matrix A=(aij)m×n saddle points are designed.