Saddle Point

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saddle point

[′sad·əl ‚pȯint]
A point where all the first partial derivatives of a function vanish but which is not a local maximum or minimum.
For a matrix of real numbers, an element that is both the smallest element of its row and the largest element of its column, or vice versa.
For a two-person, zero-sum game, an element of the payoff matrix that is the smallest element of its row and the largest element of its column, so that the corresponding strategies are optimal for each player, given the strategy chosen by the other player.

Saddle Point


a critical point of a first-order differential equation. In a neighborhood of a saddle point, four half-line integral

Figure 1

curves enter the critical point. Between the four curves there are four regions, each of which contains a family of integral curves resembling hyperbolas (see Figure l). The pattern of integral curves in a neighborhood of a saddle point is reminiscent of the contour lines of a hyperbolic paraboloid, which has the shape of a saddle—hence the name of the critical point.

References in periodicals archive ?
Noting that H(0) > 0 and dH/dq < 0 it is clear that there is at most one additional stationary value in the range 0 < [q.
Thus, there is a unique interior stationary value [[bar.
The following proposition discusses the set of stationary values and their stability.
The set of stationary values for the share of patient types in the economy, qt, consists off [[bar.
s] dependence at a constant external voltage and a stationary value of low-absorbed illumination ([hv] > [E.
9 eV) on the energy of the quanta of a stationary value of low-absorbed monochromatic illumination with hi < [E.
Indeed, near the end of the experiments, the price level was close to, though never precisely equal to, the unique stationary value [Mathematical Expression Omitted](6).
When they brought experienced subjects back to play the same game, they found that the experienced subjects always coordinated their expectations around the low-inflation stationary value for inflation and tracked this value rather closely, even after government expenditures, d, had stopped increasing.
leads to an increase in the stationary value of [[Pi].
Under the assumption that agents possess rational expectations, the higher of these two stationary values is predicted to be the limit of all equilibrium sequences for inflation starting from any initial value for [[Pi].
This implies that the range of outliers must be given independent consideration, in addition to the consideration of stationary values.