Talk:Saddle point
From Wikipedia, the free encyclopedia
| WikiProject Systems (Rated Start-Class) | |||||
|---|---|---|---|---|---|
 |
|||||
| Systems rating: | Start Class | Mid importance | Field: Dynamical systems | ||
| Please update this rating as the article progresses, or if the rating is inaccurate. Please also add comments to suggest improvements to the article. | |||||
[edit] Weak saddle point
what is a weak saddle point? --RyanTMulligan 05:40, 19 February 2007 (UTC)
[edit] x4+y4+xy & (0,0)
Sorry I can't answer the question posted by a non-signer. I have a different question myself.
I am confused. x4+y4+xy seems to have a global minimum on (0,0), according to my contour plot. Yet, the hessian (ie [0 1, 1 0]) has a positive and a negative eigenvalue (1 and -1). Hence it should be a saddle point, right? I am confused... I would hope every saddle point looks like the critical point (0,0) in the function x2-y2
--Luzsonriente 12:38, 28 December 2006 (UTC)
- Confusingly, not all saddle points look like saddles (MathWorld defines it as a stationary point which is not an extremum). Staring at it long enough, x4 + y4 + xy will have two minima on the line x = − y, substitute in and you get 2x4 − x2, differentiate to get stationary points at 8x3 − 2x = 0, which has roots at x = 0 and 4x2 = 1. --Elektron 23:53, 22 January 2007 (UTC)
[edit] Not all saddle points look like saddles, but...
... the article says: "For a function of two or more variables, the surface at a saddle-point resembles a saddle that curves up in one or more directions, and curves down in one or more other directions (like a mountain pass)", and goes on saying that in general the curve can be reduced to x^2-y^2 (which I don't know if is true). At least the first part is plain false for any saddle point not looking like a saddle, look for instance with a Java-enabled browser at [1]. Or think to a point in a surface, where the restriction of the surface in a given direction has a 1D-saddle point. In the orthogonal direction the restriction can even be a straight line, or another curve with a 1D-saddle point, or it could be everything, but we'll have a saddle point which does not look like a saddle and which does not obey the given sentence; or even, which does not curve up or down in any direction. --Blaisorblade 00:48, 9 July 2007 (UTC)
