Saddle Point


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saddle point

[′sad·əl ‚pȯint]
(geology)
col
(mathematics)
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 ?
Such saddle point systems are ubiquitous in science and engineering.
Tenders are invited for Repair/ Renovation Of Shoulders Of Road Main Gate To Saddle Point In Estate Area, At Ofba.
According to the Karuch-Kuhn-Tucker conditions, a point of equilibrium for the A interaction is a saddle point for the win formula F [2], The meaning of this result, namely of the term 'saddle point' is revealed by the answer to the question: 'What does an optimum means of expression signify in the case of both initiators of interaction [DELTA]?
They cover linear optical response and Raman spectroscopy, nonlinear optical properties, terahertz response, saddle point spectroscopy, and device application.
Under the assumptions of perfect competition and constant returns-to-scale in production, the standard RBC model exhibits an interior steady state that is a locally determinate or isolated saddle point around which there is a unique convergent equilibrium trajectory, as well as business cycles driven by exogenous shocks to economic fundamentals such as technology, preferences, and endowment.
Preconditioned Krylov subspace methods for the solutions of the saddle point systems relating to each of these problems are given in [24] and [10], respectively, for instance.
For d < 0, the potential has both a global minimum and a saddle point at non-zero [beta].
It has been proven that finding parameters corresponding to the saddle point (related to the equilibrium phenomenon) provides a satisfactory solution.
Our exact and asymptotic results make extensive use of the techniques of Flajolet and Sedgewick's book [11]: symbolic combinatorics, singularity analysis, saddle point method, and their application to the derivation of limit laws.
2010 Mathematics Subject Classification: Key words and phrases : Control functions; Periodic solutions; Hamiltonian systems with (q, p)-Laplacian; The least action principle; Saddle Point Theorem.