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Method of steepest descent

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 a contour integral in the complex plane to pass near a stationary point (saddle point), in roughly the direction of steepest descent or stationary phase. The saddle-point approximation is used with…

The case of a single non-degenerate saddle point, Extensions and generalizations & Overview

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The case of a single non-degenerate saddle point

HessianJacobianDeterminantMorse LemmaHolomorphic
18 related topics

Extensions and generalizations

Riemann–Hilbert factorizationComplex sphereAlexander ItsSolitonIntegrable models
8 related topics

Overview

MathematicsLaplace's methodComplex planeStationary pointSaddle point
15 related topics

The other cases

Catastrophe theoryOptical causticsWKB approximation
3 related topics

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Basic idea

Etymology

A simple estimate

The case of a single non-degenerate saddle point

The case of multiple non-degenerate saddle points

The other cases

Extensions and generalizations

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Method of steepest descent

Nodes59
Edges58
Triples13
Avg. degree1.97
Density0.033898
Components1

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Method of steepest descent

Top relations

related to Basic idea · 7
Method of steepest descent → Because, Im, In, Laplace's, Re, The, Then
related to Etymology · 5
Method of steepest descent → Cauchy, If, Riemann, The, Then
is a · 1
Method of steepest descent → method to approximate a complex integral of the form I

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method displaystyle steepest descent saddle point contour function phase integral equation s'' asymptotic complex det stationary integrals one functions riemann

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SubjectPredicateObjectConfidenceSrc
Method of steepest descentis amethod to approximate a complex integral of the form I0.90text
Method of steepest descentrelated to Basic ideaThe0.60section
Method of steepest descentrelated to Basic ideaBecause0.60section
Method of steepest descentrelated to Basic ideaIn0.60section
Method of steepest descentrelated to Basic ideaIm0.60section
Method of steepest descentrelated to Basic ideaRe0.60section
Method of steepest descentrelated to Basic ideaThen0.60section
Method of steepest descentrelated to Basic ideaLaplace's0.60section
Method of steepest descentrelated to EtymologyThe0.60section
Method of steepest descentrelated to EtymologyIf0.60section
Method of steepest descentrelated to EtymologyCauchy0.60section
Method of steepest descentrelated to EtymologyRiemann0.60section

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