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Math Help - Gradient - Steepest Descent

  1. #1
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    Gradient - Steepest Descent

    Hi All-

    I am having trouble understanding this.

    Start with 1 variable:

    If I have a function say, f(x) x^4-3x^3+2 that has a derivative 4x^3-9x^2 the gradient (here just the derivative) at a starting value of say x=-6 is -1188.

    (1) Does this tell me that the largest rate of change (increase) occurs in the direction of -1188? Is this X or Y?
    (2) To get steepest descent, I move in the opposite direction, towards 1188. What exactly does it mean to move in the direction of 1188? It does not seem to mean "go to point x=1188". We take x=6 - (-1188). This is the starting point to plug into the gradient. I dont think I understand.

    If you are working in 2+ variables, same questions:

    (1) what does it mean to "move in the direction of a vector"?
    (2) why take where we were (x1,y1) when working in 2 variables and subtract from that the gradient evaluated at (x1,y1)?

    I would be appreciative if someone can explain this better than my book!

    Thanks!
    Brian
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  2. #2
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    1) -1188 is your slope which is decreasing
    2) at y'=-1188 you are already in a descent
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  3. #3
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    Hi. Sorry, I dont follow. Can you explain in relation to my questions? Specifically,

    1) "what it means to move in the direction of a vector or single value in the case of a single variable"
    2) Why take your x-value you start with and subtract the gradient at that point? What is the logic of doing this?
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