Talk:Saddle point
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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)
