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A saddle point (or minimax point) on a graph of a function, is a critical point that isn’t a local extremum (i.e., it’s not a local maximum or a local minimum).
鞍点既不是极大值点，也不是极小值点，但却是一个关键点（各方向导数为0）。
Another way of stating the definition is that it is a point where the slopes (or derivatives) in orthogonal directions are all zero. However, the point is not the highest or lowest point in its neighborhood.
下图是\(z = x^2 + y^2\)，那个红色的点就是鞍点，刚好在零点位置：
还有一个概念：saddle surface
A smooth surface which has one or more saddle points is called a saddle surface.
下图是个经典的case，叫做monkey saddle，来自\(z = x^3-3xy^2\)：
If the name seems a bit random, try imagining it as a saddle for a monkey, with a place for both legs and another place for the tail.
本文链接：https://cs.pynote.net/math/202210221/
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