Some asymptotic representations can then be derived by a standard application of the method of steepest descent.
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An asymptotic evaluation is then possible along the lines of the linear stationary phase / steepest descent method.
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The " nearest " minimum is that minimum which lies at the end of the path of steepest descent.
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Thus, every iteration of these steepest descent methods is a bit cheaper compared to that for the conjugate gradient methods.
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A common variant uses a constant-size, small simplex that roughly follows the gradient direction ( which gives steepest descent ).
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An autoencoder is often trained using one of the many variants of backpropagation ( such as conjugate gradient method, steepest descent, etc . ).
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The contour of steepest descent has a minimax property, see . described some other unpublished notes of Riemann, where he used this method to derive the Riemann-Siegel formula.
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Lucky invented a way to adaptively undo the smearing effects by automatic adjustment of a variable filter, using a tapped equalizer used a steepest descent algorithm to minimize distortion.
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The method of steepest descent was first published by, who used it to estimate Bessel functions and pointed out that it occurred in the unpublished note about hypergeometric functions.
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Asymptotic expansions typically arise in the approximation of certain integrals ( Laplace's method, saddle-point method, method of steepest descent ) or in the approximation of probability distributions ( Edgeworth series ).
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