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...

direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely...

Laplace's method and the method of steepest descent, but Laplace's contribution precedes the others. The main idea of stationary phase methods relies on...

}{N}}}e^{-N}={\sqrt {2\pi N}}N^{N}e^{-N}.} Mathematics portal Method of stationary phase Method of steepest descent Large deviations theory Laplace principle (large...

Thus, every iteration of these steepest descent methods is a bit cheaper compared to that for the conjugate gradient methods. However, the latter converge...

to the steepest descent direction at least every N iterations, or sooner if progress stops. However, resetting every iteration turns the method into steepest...

Method of matched asymptotic expansions Method of steepest descent Old quantum theory Perturbation methods Quantum tunneling Slowly varying envelope approximation...

q=q_{0}} . These integrals can be approximated by the method of steepest descent. For small values of the Planck constant, f can be expanded about its minimum...

Boosting" (PDF). Lambers, Jim (2011–2012). "The Method of Steepest Descent" (PDF). Note: in case of usual CART trees, the trees are fitted using least-squares...

this sequence has similar convergence properties as steepest descent. No improvement after one cycle of line search along coordinate directions implies a...

Laplace's method Stationary phase approximation Method of dominant balance Method of steepest descent Jahnke, Hans Niels (2003). A history of analysis...

prove the validity of asymptotic approximations for integrals. Rigorous treatments of the method of steepest descent and the method of stationary phase...

extension of the steepest descent method for getting uniform asymptotic expansions in the case of coalescing saddle points. The method was published in...

Stochastic hill climbing is a variant of the basic hill climbing method. While basic hill climbing always chooses the steepest uphill move, "stochastic hill climbing...

he developed a steepest descent algorithm, based on work by Cauchy. This became a foundational example of modern gradient descent methods. In 1947 Curry...

(which gives steepest descent). Visualize a small triangle on an elevation map flip-flopping its way down a valley to a local bottom. This method is also known...

partition of unity can be used to show the existence of a Riemannian metric on an arbitrary manifold. Method of steepest descent employs a partition of unity...

F ′ ( ζ ) = 0 {\displaystyle F^{'}(\zeta )=0} . See also the method of steepest descent. Melczer 2021, pp. vii and ix. Pemantle and Wilson 2013, pp. xi...

transform Harmonic conjugate Hilbert's inequality Method of steepest descent Montel's theorem Periodic points of complex quadratic mappings Pick matrix Runge...

northern hemisphere of the moon. Electroacoustic phenomena Ion vibration current Magnetic refrigeration Method of steepest descent Rotational Brownian...

lack of differentiability rules out conventional smooth optimization techniques like the steepest descent method and the conjugate gradient method, but...

the author of Hadamard Expansions and Hyperasymptotic Evaluation: An Extension of the Method of Steepest Descent as well as the co-author of Asymptotics...

This method of evaluation of Z {\displaystyle Z} around the saddle point ω 0 {\displaystyle \omega _{0}} is known as the method of steepest descent. One...

for the minimum of the objective function along the steepest descent direction, known as Cauchy point. If the Cauchy point is outside of the trust region...

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

representations can then be derived by a standard application of the method of steepest descent. The Bell numbers form a logarithmically convex sequence....

method of stationary phase and the method of steepest descent applicable to exponential integrals. By analogy with the classical asymptotic methods,...

through method of steepest descent. For the periodic structures such as phased arrays and frequency selective surfaces, series acceleration methods such...

coordinated pre- and post-smoothing. However, preconditioned steepest descent and flexible CG methods for SPD linear systems and LOBPCG for symmetric eigenvalue...

applying the method of steepest descent to this integral to give an asymptotic expansion for the error term R(s) as a series of negative powers of Im(s). In...