Method of steepest descent
（重定向自Saddle point approximation）
![An illustration of Complex Morse Lemma](/Images/godic/202502/08/page1-220px-Complex_Morse_Lemma_Illustration.pdf1158.jpg")
![An illustration to the derivation of equation (8)](/Images/godic/202502/08/page1-220px-Illustration_To_Derivation_Of_Asymptotic_For_Saddle_Point_Integration.pdf1159.jpg")
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.