Please explain the method of steepest descent?

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The method of steepest descent, also known as the saddle point method, is used for optimizing functions by following the gradient to find local maxima or minima. It is particularly useful for approximating certain contour integrals. Although resources like Wikipedia provide general information, specific applications may require deeper understanding and context. The discussion highlights a need for step-by-step guidance, especially for those unfamiliar with the method. Further research and clarification on the integral in question are recommended for better comprehension.
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I am not understanding how to use the method of steepest descent aka the saddle point method. Any help would be appreciated, especially step-by-step explanation!
 
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wishfulthinking said:
I am not understanding how to use the method of steepest descent aka the saddle point method. Any help would be appreciated, especially step-by-step explanation!

The method of steepest descent, or gradient descent, is a means of using the gradient of a function to perform an optimization:

http://en.wikipedia.org/wiki/Gradient_descent

You can find many more articles on such a procedure by Googling 'method of steepest descent' or 'method of gradient descent'.
 
Thanks, I did Google the method, but I'm still not quite sure how to use it.
 
wishfulthinking said:
Thanks, I did Google the method, but I'm still not quite sure how to use it.
Well, how familiar are you with using root finding algorithms on single variable equations, like finding the roots of polynomials?

Roughly speaking, steepest descent is an analogous method for functions of two or more variables, where you are trying to find the point at which the function reaches a local maximum or minimum.
 
Thanks for taking the time out to reply. Specifically, I'm being asked to approximate an integral using the method. I've never learned this before and it's not in our textbook. My teacher said to look for outside resources, I'm just not understanding it and was hoping someone could explain it to me.
 
wishfulthinking said:
Thanks for taking the time out to reply. Specifically, I'm being asked to approximate an integral using the method. I've never learned this before and it's not in our textbook. My teacher said to look for outside resources, I'm just not understanding it and was hoping someone could explain it to me.

Well, this technique is used to approximate certain contour integrals, as discussed here:

http://en.wikipedia.org/wiki/Method_of_steepest_descent

Since you know more about the type of integral you are trying to approximate, you're the one best suited to do the research. ;)
 

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