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- Method_of_steepest_descent abstract "In mathematics, the method of steepest descent or stationary phase method 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 integrals in the complex plane, whereas Laplace’s method is used with real integrals.The integral to be estimated is often of the formwhere C is a contour and λ is large. One version of the method of steepest descent deforms the contour of integrationso that it passes through a zero of the derivative g′(z) in such a way that on the contour g is (approximately) real and has a maximum at the zero.The method of steepest descent was first published by Debye (1909), who used it to estimate Bessel functions and pointed out that it occurred in the unpublished note Riemann (1863) about hypergeometric functions. The contour of steepest descent has a minimax property, see Fedoryuk (2001). Siegel (1932) described some other unpublished notes of Riemann, where he used this method to derive the Riemann-Siegel formula.".
- Method_of_steepest_descent wikiPageID "27082137".
- Method_of_steepest_descent wikiPageRevisionID "605414284".
- Method_of_steepest_descent first "M V".
- Method_of_steepest_descent hasPhotoCollection Method_of_steepest_descent.
- Method_of_steepest_descent id "Saddle_point_method".
- Method_of_steepest_descent last "Fedoryuk".
- Method_of_steepest_descent subject Category:Asymptotic_analysis.
- Method_of_steepest_descent subject Category:Perturbation_theory.
- Method_of_steepest_descent comment "In mathematics, the method of steepest descent or stationary phase method 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.".
- Method_of_steepest_descent label "Method of steepest descent".
- Method_of_steepest_descent label "Metoda najszybszego spadku".
- Method_of_steepest_descent label "Méthode du point col".
- Method_of_steepest_descent label "Метод перевала".
- Method_of_steepest_descent sameAs Méthode_du_point_col.
- Method_of_steepest_descent sameAs Metoda_najszybszego_spadku.
- Method_of_steepest_descent sameAs m.02zr_k.
- Method_of_steepest_descent sameAs Q1997812.
- Method_of_steepest_descent sameAs Q1997812.
- Method_of_steepest_descent wasDerivedFrom Method_of_steepest_descent?oldid=605414284.
- Method_of_steepest_descent isPrimaryTopicOf Method_of_steepest_descent.