Saddle Point

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A Saddle Point is a surface point that ...



References

2017

  • (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/saddle_point Retrieved:2017-6-8.
    • In mathematics, a saddle point or minimax point [1] is a point on the surface of the graph a function where the slopes (derivatives) of orthogonal function components defining the surface become zero (a stationary point) but are not a local extremum on both axes. [2] The saddle point will always occur at a relative minimum along one axial direction (between peaks) and at a relative maximum along the crossing axis.

      The name derives from the fact that the prototypical example in two dimensions is a surface that curves up in one direction, and curves down in a different direction, resembling a riding saddle or a mountain pass between two peaks forming a landform saddle. In terms of contour lines, a saddle point in two dimensions gives rise to a contour graph or trace that appears to intersect itself—such conceptually might form a 'figure eight' around both peaks; assuming the contour graph is at the very 'specific altitude' of the saddle point in three dimensions.

  1. Howard Anton, Irl Bivens, Stephen Davis (2002): Calculus, Multivariable Version, p. 844
  2. Chiang, Alpha C., Fundamental Methods of Mathematical Economics, 3rd edition, 1984, p. 312.

2014