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Please explain the method of steepest descent?

  1. Feb 11, 2015 #1
    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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  3. Feb 11, 2015 #2

    SteamKing

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    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'.
     
  4. Feb 11, 2015 #3
    Thanks, I did Google the method, but I'm still not quite sure how to use it.
     
  5. Feb 11, 2015 #4

    SteamKing

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    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.
     
  6. Feb 11, 2015 #5
    Thanks for taking the time out to reply. Specifically, I'm being asked to approximate an integral using the method. Ive 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.
     
  7. Feb 11, 2015 #6

    SteamKing

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    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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