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In mathematics, the method of steepest descent or saddle-point method is an extension of Laplace's method for approximating an integral, where one deforms...

In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions...

circle method. Walter Hayman's 1956 paper A Generalisation of Stirling's Formula is considered one of the earliest examples of the saddle-point method. In...

These solutions may be minima, maxima, or saddle points; see section "Several variables" in Critical point (mathematics) and also section "Geometric interpretation"...

test is a method in multivariable calculus used to determine if a critical point of a function is a local minimum, maximum or saddle point. Suppose that...

\mathrm {d} z.} This line integral can then be approximated using the saddle-point method with an appropriate choice of contour radius r = r n {\displaystyle...

(x)=e^{-1/(1-x^{2})}\mathbf {1} _{\{|x|<1\}}} from above can be analyzed by a saddle-point method, and decays asymptotically as | k | − 3 / 4 e − | k | {\displaystyle...

arise in the approximation of certain integrals (Laplace's method, saddle-point method, method of steepest descent) or in the approximation of probability...

frequency (roughly as k − 2 / 3 {\displaystyle k^{-2/3}} ). Using the saddle point method, we can show that A k ∼ 4 π 3 / 2 3 κ exp ⁡ ( − 3 κ 2 + π 2 4 κ )...

of its power series, apply this method to a large number of combinatorial examples, and study the saddle-point method of contour integration for handling...

 267. ISBN 0-387-96058-9. Walsh, G.R. (1975). "Saddle-point Property of Lagrangian Function". Methods of Optimization. New York, NY: John Wiley & Sons...

A saddle is a supportive structure for a rider of an animal, fastened to an animal's back by a girth. The most common type is equestrian. However, specialized...

A bicycle saddle, sometimes called a bicycle seat, is one of five contact points on an upright bicycle, the others being the two pedals and the two handles...

sufficient condition for a saddle point problem to have a unique solution that depends continuously on the input data. Saddle point problems arise in the discretization...

western saddle or Australian Stock Saddle, there is no horn or other design elements that stick out above the main tree of the saddle. The English saddle is...

include: Homoclinic bifurcation in which a limit cycle collides with a saddle point. Homoclinic bifurcations can occur supercritically or subcritically....

Bronc riding, either bareback bronc or saddle bronc competition, is a rodeo event that involves a rodeo participant riding a bucking horse (sometimes called...

multipliers. The Karush–Kuhn–Tucker theorem is sometimes referred to as the saddle-point theorem. The KKT conditions were originally named after Harold W. Kuhn...

analysis. The method is named after M. S. Bartlett who first proposed it. Bartlett’s method consists of the following steps: The original N point data segment...

reach the saddle point, relaxing in the perpendicular hyperplane between each "jump" (activation) in this direction. Chain-of-state methods can be used...